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Type 'q()' to quit R. > library(Bessel) > > #### Test cases for the Bessel functions I(), J(), K(), Y() > #### ----------------------------------- > > all.eq <- function(x,y, tol=1e-15,...) all.equal(x, rep_len(y,length(x)), tol=tol, ...) > > (op <- options(width=max(99, getOption("width")), warn = 0, + nwarnings = 999, warnPartialMatchArgs = FALSE)) # all.equal(*,*, tol = ..) $width [1] 80 $warn [1] 0 $nwarnings [1] 50 $warnPartialMatchArgs [1] FALSE > > isOSunix <- .Platform$OS.type == "unix" > windows <- !isOSunix > > stop_or_w <- if(isOSunix) stop else warning > > ### --- For real arguments -- Comparisons with bessel[IJYK]() > > x <- c(1e-6, 0.1, 1:10, 20, 100, 200)# larger x : less (relative) accuracy (??) > nus <- c(-6, -5.9, -1.1, .1, 1:4, 10, 20) > ## From R 2.10.1 (or 2.10.0 patched, >= Nov.23 2009) on, this works, previously > ## R"s besselJ() had an inaccuracy that we have corrected here ! > ## FIXME ? ---- we currently need to fudge for negative nu > ## note that (nu != -6 but nu ~ -6, |x| << |nu|) is still unstable, > ## since sin(nu*pi) ~ 0 (but not exactly!) and besselK() is large > nS <- 10 > for(F in c("I","J","K","Y")) { + cat("\n", F," --- nu : ") + zF <- get(paste0("Bessel", F)) # our pkg 'Bessel' + FF <- get(paste0("bessel", F)) # base R + stopifnot(is.function(zF), is.function(FF)) + for(nu in nus) { + x. <- x + spec <- FALSE ## nu < 0 && F %in% c("I","J") + cat(format(nu), if(spec)"* " else " ", sep="") + zr <- zF(x., nu, nSeq = nS) + rr <- outer(x., nu+ sign(nu)*(seq_len(nS)-1), FF) + stopifnot(all.equal(zr, rr, tol = 500e-16)) + }; cat("\n") + } I --- nu : -6 -5.9 -1.1 0.1 1 2 3 4 10 20 J --- nu : -6 -5.9 -1.1 0.1 1 2 3 4 10 20 K --- nu : -6 -5.9 -1.1 0.1 1 2 3 4 10 20 Y --- nu : -6 -5.9 -1.1 0.1 1 2 3 4 10 20 > > zr0 <- if(file.exists(sf <- "zr_IJKY.rds")) { readRDS(sf) + } else { print(saveRDS(zr, file=sf, version=2)) ; zr } > > ## Show: > all.equal(zr, zr0, tol = 0) [1] TRUE > > if(!isTRUE(ae <- all.equal(zr, zr0, tol = 1e-12))) + stop_or_w(ae) > > > ## "limit z -> 0 does not exist (there are many complex "Inf"s), > ## but for z = real, z >=0 is -Inf > stopifnot(BesselY(0,1) == -Inf,# == besselY(0,1), + is.nan(BesselY(0+0i, 1))) > > ### *Large* arguments , > ### However, base::bessel*(): only I() and K() have 'expon.scaled' > > x <- c(1000*(1:20), 20000*2^(1:20)) > str(rI <- BesselI(x, 10, nSeq = 5, expon.scaled=TRUE)) num [1:40, 1:5] 0.012 0.0087 0.00716 0.00623 0.00559 ... There were 20 warnings (use warnings() to see them) > > if(getRversion() >= "2.8.2") { ## besselI(), besselJ() with larger working range + ri2 <- outer(x, 10+seq_len(5)-1, besselI, expon.scaled=TRUE) + stopifnot(all.equal(rI[1:20,], ri2[1:20,], tol = 8e-16)) + stopifnot(all.equal(rI[1:35,], ri2[1:35,], tol = 0.04))# base::besselI is underflowing to zero + } ## R >= 2.8.2 > > rI0 <- if(file.exists(sf <- "r_I.rds")) { readRDS(sf) + } else { print(saveRDS(rI, sf, version=2)) ; rI } > > ri2.0 <- if(file.exists(sf <- "r_i2.rds")) { readRDS(sf) + } else { print(saveRDS(ri2, sf, version=2)); ri2 } > > ## Show the closeness (on different platforms): > all.equal(rI, rI0, tolerance = 0) [1] TRUE > all.equal(ri2, ri2.0, tolerance = 0) [1] TRUE > > stopifnot(exprs = { + all.equal(rI, rI0, tolerance = if(windows) 1e-10 else 1e-14) + all.equal(ri2, ri2.0, tolerance = if(windows) 1e-10 else 1e-14) + }) > > > ## e.g. this x is too large: > x. <- 1310720000 > BesselI(x., 10, nSeq = 5, expon.scaled=TRUE) [,1] [,2] [,3] [,4] [,5] [1,] NaN NaN NaN NaN NaN Warning message: In BesselI(x., 10, nSeq = 5, expon.scaled = TRUE) : 'zbesi(1.31072e+09 + 0i, nu=10)' -> ierr=4: |z| or nu too large > ## [,1] [,2] [,3] [,4] [,5] > ## [1,] NaN NaN NaN NaN NaN > ## Warning message: > ## In BesselI(1310720000, 10, nSeq = 5, expon.scaled = TRUE) : > ## 'zbesi(1.31072e+09 + 0i, nu=10)' -> ierr=4: |z| or nu too large > stopifnot(exprs = { + (bI <- besselIasym(x., 10:14, expon.scaled=TRUE)) > 0 + all.eq(bI, bI1 <- besselIasym (x., 10:14, expon.scaled=TRUE, k.max=1), tol=4e-15)# got 1.63e-15 + all.eq(bI, bI2 <- besselIasym (x., 10:14, expon.scaled=TRUE, k.max=2)) + all.eq(bI, bI1n<- besselI.nuAsym(x., 10:14, expon.scaled=TRUE, k.max=1)) + # here, k. = 1 is slightly better + all.eq(bI, bI2n<- besselI.nuAsym(x., 10:14, expon.scaled=TRUE, k.max=2)) + all.eq(bI, bI4n<- besselI.nuAsym(x., 10:14, expon.scaled=TRUE, k.max=4)) + }) > > ## How good are the different 'k's > library(Rmpfr)# {it has been _import_ed anyway in Bessel} Loading required package: gmp Attaching package: 'gmp' 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 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 > k.max <- 5 > bImp <- new("mpfr", unlist(lapply(0:k.max, function(k) + besselI.nuAsym(mpfr(x., 256), 10, expon.scaled=TRUE, k.max=k)), + recursive = FALSE)) > cbind(k = 0:(k.max-1), err.k = asNumeric(bImp - bImp[k.max+1])[-(k.max+1)]) k err.k [1,] 0 -1.050885e-15 [2,] 1 -4.509909e-25 [3,] 2 -3.584154e-34 [4,] 3 -4.187191e-43 [5,] 4 -6.469011e-52 > ## k err.k > ## 0 -1.051e-15 > ## 1 -4.510e-25 > ## 2 -3.584e-34 > ## 3 -4.187e-43 > ## 4 -6.469e-52 > > > ## K(): Bessel:: vs R base:: ------------ > > str(rK <- BesselK(x, 10, nSeq = 5, expon.scaled=TRUE)) # our Bessel pkg [=> 20 warnings !] num [1:40, 1:5] 0.0417 0.0287 0.0233 0.0201 0.0179 ... There were 20 warnings (use warnings() to see them) > rK2 <- outer(x, 10+seq_len(5)-1, + besselK, expon.scaled=TRUE) # base R > stopifnot(all.equal(rK[1:35,], rK2[1:35,], tol = 8e-16)) > > cbind(x, local({ M <- rK; colnames(M) <- paste0("nu=",10+seq_len(ncol(M))-1); M })) x nu=10 nu=11 nu=12 nu=13 nu=14 [1,] 1000 4.165905e-02 4.209855e-02 4.258522e-02 4.312059e-02 4.370635e-02 [2,] 2000 2.873243e-02 2.888364e-02 2.905015e-02 2.923224e-02 2.943017e-02 [3,] 3000 2.326581e-02 2.334737e-02 2.343703e-02 2.353487e-02 2.364100e-02 [4,] 4000 2.006524e-02 2.011797e-02 2.017589e-02 2.023903e-02 2.030744e-02 [5,] 5000 1.790221e-02 1.793984e-02 1.798114e-02 1.802615e-02 1.807488e-02 [6,] 6000 1.631526e-02 1.634384e-02 1.637519e-02 1.640934e-02 1.644630e-02 [7,] 7000 1.508707e-02 1.510972e-02 1.513456e-02 1.516161e-02 1.519088e-02 [8,] 8000 1.410010e-02 1.411862e-02 1.413893e-02 1.416104e-02 1.418495e-02 [9,] 9000 1.328450e-02 1.330001e-02 1.331701e-02 1.333552e-02 1.335554e-02 [10,] 10000 1.259580e-02 1.260904e-02 1.262354e-02 1.263933e-02 1.265641e-02 [11,] 11000 1.200418e-02 1.201565e-02 1.202822e-02 1.204189e-02 1.205668e-02 [12,] 12000 1.148879e-02 1.149885e-02 1.150987e-02 1.152187e-02 1.153483e-02 [13,] 13000 1.103454e-02 1.104346e-02 1.105323e-02 1.106387e-02 1.107536e-02 [14,] 14000 1.063024e-02 1.063821e-02 1.064696e-02 1.065647e-02 1.066675e-02 [15,] 15000 1.026735e-02 1.027454e-02 1.028242e-02 1.029099e-02 1.030026e-02 [16,] 16000 9.939252e-03 9.945776e-03 9.952927e-03 9.960706e-03 9.969113e-03 [17,] 17000 9.640723e-03 9.646679e-03 9.653206e-03 9.660307e-03 9.667981e-03 [18,] 18000 9.367571e-03 9.373037e-03 9.379027e-03 9.385543e-03 9.392584e-03 [19,] 19000 9.116395e-03 9.121434e-03 9.126957e-03 9.132963e-03 9.139454e-03 [20,] 20000 8.884397e-03 8.889062e-03 8.894175e-03 8.899735e-03 8.905744e-03 [21,] 40000 6.274389e-03 6.276036e-03 6.277841e-03 6.279803e-03 6.281923e-03 [22,] 80000 4.433898e-03 4.434480e-03 4.435117e-03 4.435811e-03 4.436559e-03 [23,] 160000 3.134262e-03 3.134468e-03 3.134693e-03 3.134938e-03 3.135203e-03 [24,] 320000 2.215913e-03 2.215985e-03 2.216065e-03 2.216152e-03 2.216245e-03 [25,] 640000 1.566765e-03 1.566790e-03 1.566819e-03 1.566849e-03 1.566882e-03 [26,] 1280000 1.107827e-03 1.107836e-03 1.107846e-03 1.107857e-03 1.107868e-03 [27,] 2560000 7.833366e-04 7.833398e-04 7.833433e-04 7.833472e-04 7.833513e-04 [28,] 5120000 5.538972e-04 5.538984e-04 5.538996e-04 5.539010e-04 5.539024e-04 [29,] 10240000 3.916626e-04 3.916630e-04 3.916634e-04 3.916639e-04 3.916644e-04 [30,] 20480000 2.769466e-04 2.769467e-04 2.769469e-04 2.769471e-04 2.769472e-04 [31,] 40960000 1.958306e-04 1.958306e-04 1.958307e-04 1.958307e-04 1.958308e-04 [32,] 81920000 1.384730e-04 1.384731e-04 1.384731e-04 1.384731e-04 1.384731e-04 [33,] 163840000 9.791520e-05 9.791520e-05 9.791521e-05 9.791522e-05 9.791523e-05 [34,] 327680000 6.923649e-05 6.923649e-05 6.923649e-05 6.923650e-05 6.923650e-05 [35,] 655360000 4.895759e-05 4.895759e-05 4.895759e-05 4.895759e-05 4.895759e-05 [36,] 1310720000 NaN NaN NaN NaN NaN [37,] 2621440000 NaN NaN NaN NaN NaN [38,] 5242880000 NaN NaN NaN NaN NaN [39,] 10485760000 NaN NaN NaN NaN NaN [40,] 20971520000 NaN NaN NaN NaN NaN > > > ## Behaviour------------- x --> 0 ----------------------------- > ## From examples in example(besselI): ~/R/D/r-devel/R/src/library/base/man/Bessel.Rd > > ## J(): > nus <- c(0:5, 10, 20) > x0 <- 2^seq(-16, 5, length.out=256) > rbJ <- vapply(sort(c(nus, nus+0.5)), besselJ, x=x0, FUN.VALUE=x0) > rBJ <- vapply(sort(c(nus, nus+0.5)), BesselJ, z=x0, FUN.VALUE=x0) > stopifnot(all.equal(rbJ, rBJ, tol=1e-14)) # Lx 64b: 1.728e-15 > > ## K(): > x0 <- 2^seq(-10, 8, length.out=256) > rbK <- vapply(sort(c(nus, nus+0.5)), besselK, x=x0, FUN.VALUE=x0) > rBK <- vapply(sort(c(nus, nus+0.5)), BesselK, z=x0, FUN.VALUE=x0) > stopifnot(all.equal(rbK, rBK, tol=1e-14)) # Lx 64b: 1.3257e-15 > > ## TODO?: expon.scale here > > ## Y(): > x <- seq(1/32, 40, by=1/32) > rbY <- vapply(sort(c(nus, nus+0.5)), besselY, x=x, FUN.VALUE=x) > rBY <- vapply(sort(c(nus, nus+0.5)), BesselY, z=x, FUN.VALUE=x) > stopifnot(all.equal(rbY, rBY, tol=1e-14)) # Lx 64b: 1.92e-16 > > > ###--------------------- Complex Arguments ------------------------------ > > besselIexpos <- function(z, nu, expoS = TRUE) { + drop(cbind(z, + bI = if(is.numeric(z)) besselI(z, nu, expon.scaled=expoS) else NA + , BI = BesselI(z, nu, expon.scaled=expoS) + , bIa.0 = besselIasym(z, nu, k.max=0, expon.scaled=expoS) + , bIa.1 = besselIasym(z, nu, k.max=1, expon.scaled=expoS) + , bIa.2 = besselIasym(z, nu, k.max=2, expon.scaled=expoS) + , bIa.3 = besselIasym(z, nu, k.max=3, expon.scaled=expoS) + , bIa.4 = besselIasym(z, nu, k.max=4, expon.scaled=expoS) + , bIa.6 = besselIasym(z, nu, k.max=6, expon.scaled=expoS) + , bIa.9 = besselIasym(z, nu, k.max=9, expon.scaled=expoS) + , bIa.19 =besselIasym(z, nu, k.max=19,expon.scaled=expoS) + , bIna.0 = besselI.nuAsym(z, nu, k.max=0, expon.scaled=expoS) + , bIna.1 = besselI.nuAsym(z, nu, k.max=1, expon.scaled=expoS) + , bIna.2 = besselI.nuAsym(z, nu, k.max=2, expon.scaled=expoS) + , bIna.3 = besselI.nuAsym(z, nu, k.max=3, expon.scaled=expoS) + , bIna.4 = besselI.nuAsym(z, nu, k.max=4, expon.scaled=expoS) + , bIna.5 = besselI.nuAsym(z, nu, k.max=5, expon.scaled=expoS) + )) + } > > > " + z := 10000 + 10000 I + N[Exp[-Re[z]] * BesselI[10, z]] + " # -- see ../misc/MM_NUMERICS_Bessel/Bessel_I.txt [1] "\nz := 10000 + 10000 I\nN[Exp[-Re[z]] * BesselI[10, z]]\n" > I10k1i.true <- -0.0033357343879205302021 + 0.0002661591388785316826i # from M. > bI10k1i <- besselIexpos(10000*(1+1i), nu=10) ## all look good now: > cbind(Mod(bI10k1i[-(1:2)] - I10k1i.true)/Mod(I10k1i.true)) [,1] BI 1.619984e-17 bIa.0 3.531183e-03 bIa.1 6.104547e-06 bIa.2 6.746205e-09 bIa.3 5.233303e-12 bIa.4 2.877969e-15 bIa.6 2.336374e-16 bIa.9 2.336374e-16 bIa.19 2.336374e-16 bIna.0 8.839029e-06 bIna.1 3.525725e-10 bIna.2 1.083859e-12 bIna.3 1.073534e-12 bIna.4 1.073534e-12 bIna.5 1.073534e-12 > ## BI 1.619984e-17 > ## bIa.0 3.531183e-03 > ## bIa.1 6.104547e-06 > ## bIa.2 6.746205e-09 > ## bIa.3 5.233303e-12 > ## bIa.4 2.877969e-15 > ## bIa.6 2.336374e-16 < has converged: > ## bIa.9 2.336374e-16 > ## bIa.19 2.336374e-16 > ## bIna.0 8.839029e-06 > ## bIna.1 3.525725e-10 > ## bIna.2 1.083583e-12 > ## bIna.3 1.073230e-12 -- does not get better from here ?? > ## bIna.4 1.073230e-12 [also not better for larger nu=200, see below] > ## bIna.5 1.073230e-12 > > bInms <- names(bI10k1i[-(1:2)]) > nIa.0 <- bInms[bInms != "bIa.0"] > n0nms <- bInms[-grep("\\.0$", bInms)] > n1nms <- n0nms[-grep("\\.1$", n0nms)] > nIhi <- -c(1:2, 4:8, 12L) > stopifnot(exprs = { + all.equal( bI10k1i[["BI"]], I10k1i.true, tol=1e-15)# 1.62e-17 [Linux F28 64bit] + all.eq(unname(bI10k1i[bInms]), I10k1i.true, tol = .0006)# 0.0002364 (L.64b) + all.eq(unname(bI10k1i[n0nms]), I10k1i.true, tol = 1e-6) # 4.7e-7 (L.64b) + all.eq(unname(bI10k1i[n1nms]), I10k1i.true, tol = 2e-9) # 6.14e-10 (L.64b) + }) > > bI10k1i_100 <- besselIexpos(10000*(1+1i), nu=100) ## "large nu" > bI10k1i_200 <- besselIexpos(10000*(1+1i), nu=200) ## "large nu" > ## M. > I10k1i_1c.true <- -0.0025759149166597967497 - 0.0004365793917996836889i > I10k1i_2c.true <- -0.00074969703502560811294 - 0.0009802957040275765138i > ## Overview ... *I.nuAsym() not really good for larger k -- "large nu" did *not* help > signif(cbind("nu=100" = Mod(bI10k1i_100[bInms] / I10k1i_1c.true - 1), + "nu=200" = Mod(bI10k1i_200[bInms] / I10k1i_2c.true - 1)), 3) nu=100 nu=200 BI 2.88e-16 7.19e-13 bIa.0 4.01e-01 2.33e+00 bIa.1 7.38e-02 1.95e+00 bIa.2 8.88e-03 1.00e+00 bIa.3 7.94e-04 3.71e-01 bIa.4 5.65e-05 1.08e-01 bIa.6 1.69e-07 5.37e-03 bIa.9 1.02e-11 2.17e-05 bIa.19 2.64e-16 1.32e-15 bIna.0 8.84e-06 8.84e-06 bIna.1 3.53e-10 3.53e-10 bIna.2 1.69e-12 1.22e-12 bIna.3 1.67e-12 1.21e-12 bIna.4 1.67e-12 1.21e-12 bIna.5 1.67e-12 1.21e-12 > > stopifnot(exprs = { + all.equal( bI10k1i_100[["BI"]], I10k1i_1c.true, tol = 2e-15)# 3.55e-16 [Linux F28 64bit] + all.eq(unname(bI10k1i_100[bInms]), I10k1i_1c.true, tol = .05 )# 0.03166 (L.64b) + all.eq(unname(bI10k1i_100[nIa.0]), I10k1i_1c.true, tol = .01 )# 0.00596 (L.64b) + all.eq(unname(bI10k1i_100[-(1:7)]),I10k1i_1c.true, tol = 5e-5 )# 6.55e-6 (L.64b) + all.eq(unname(bI10k1i_100[nIhi ]), I10k1i_1c.true, tol = 8e-8 )# 1.88e-8 (L.64b) + + ## and here it's even worse [ why o why o why ??? ] + all.equal( bI10k1i_200[["BI"]], I10k1i_2c.true, tol = 2e-12)# 7.19e-13 [Linux F28 64bit] + all.eq(unname(bI10k1i_200[bInms]), I10k1i_2c.true, tol = 0.5 ) # 0.325 (L.64b) << !!!!! + all.eq(unname(bI10k1i_200[nIa.0]), I10k1i_2c.true, tol = .01 )# 0.00596 (L.64b) + all.eq(unname(bI10k1i_200[nIhi ]), I10k1i_2c.true, tol = .003 )# 5.99e-4 (L.64b) + }) > > > ## For now, another smaller |z| example only: > z20_5 <- 20 + 5i > I_10.z20_5 <- 0.0056200852295677786309-0.0060677028739147767132i # from M. > stopifnot(exprs = { + all.equal(BesselI (z20_5, 10, expon.scaled=TRUE), I_10.z20_5, + tol = 1e-15) # 2.345e-16 [Lnx_64b] + all.equal(besselIs(z20_5, 10, expon.scaled=TRUE), I_10.z20_5, + tol = 8e-15) # 1.049e-15 [Lnx_64b] + ## with negative real part: + all.equal(BesselI (-20+5i, 10, expon.scaled=TRUE), Conj(I_10.z20_5), + tol = 1e-15) # 2.345e-16 [Lnx_64b] ^^^^ + all.equal(besselIs(-20+5i, 10, expon.scaled=TRUE), Conj(I_10.z20_5), + tol = 1e-14) # 2.759e-15 [Lnx_64b] ^^^^ + }) Warning messages: 1: In FUN(X[[i]], ...) : 'nterm=800' may be too small for 20+5i 2: In FUN(X[[i]], ...) : 'nterm=800' may be too small for -20+5i > bInuAs.20_5 <- sapply(0:5, function(k.m) besselI.nuAsym(z20_5, 10, k.max=k.m)) > bInuAsEX20_5 <- sapply(0:5, function(k.m) besselI.nuAsym(z20_5, 10, k.max=k.m, expon.scale=TRUE)) > print(cbind(c(bInuAs.20_5, # converging slowly to true : + True=exp(20)*I_10.z20_5)), digits=10) [,1] 2716085.092-2932109.229i 2726489.289-2943857.203i 2726663.352-2943854.903i 2726669.530-2943840.053i 2726669.775-2943838.416i 2726669.760-2943838.263i True 2726669.749-2943838.251i > print(cbind(c(bInuAsEX20_5, # converging slowly to true : + True=I_10.z20_5)), digits=10) [,1] 0.005598268626-0.006043527558i 0.005619713274-0.006067741939i 0.005620072046-0.006067737197i 0.005620084778-0.006067706590i 0.005620085284-0.006067703214i 0.005620085252-0.006067702900i True 0.005620085230-0.006067702874i > stopifnot(exprs = { + (err <- Mod(bInuAs.20_5*exp(-20) / I_10.z20_5 - 1)) < 6*10^-c(3,5:9) + all.equal(err, Mod(bInuAsEX20_5 / I_10.z20_5 - 1), tol= 1e-9) # 2.5e-12 + }) > > z0 <- round(c(c(.5, 1, 2, 5)/10, 1:10)*1000) > z <- list(1, 2-1i, 1+1i, 1-2i) > names(z) <- local({ + c <- format(lapply(z, function(.) if(Im(.)) . else Re(.))) + ifelse(c == "1", "N", paste0("N*(",c,")")) # (no longer UTF multiplication dot) + }) > z <- lapply(z, function(f) f*z0) > > Iz <- lapply(z, besselIexpos, nu = 10) > ## ---- for now: fine with 'numeric', not at all ok with complex !!!! > print(lapply(Iz, t), digits=4) $N [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] z 50.000000 100.00000 200.00000 500.00000 1.000e+03 2.000e+03 3.000e+03 4.000e+03 5.000e+03 bI 0.020668 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 BI 0.020668 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIa.0 0.056419 0.03989 0.02821 0.01784 1.262e-02 8.921e-03 7.284e-03 6.308e-03 5.642e-03 bIa.1 0.000141 0.02000 0.02117 0.01606 1.199e-02 8.698e-03 7.163e-03 6.229e-03 5.586e-03 bIa.2 0.027647 0.02486 0.02203 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIa.3 0.019051 0.02410 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIa.4 0.020937 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIa.6 0.020671 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIa.9 0.020668 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIa.19 0.020668 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIna.0 0.020621 0.02415 0.02196 0.01614 1.200e-02 8.700e-03 7.163e-03 6.229e-03 5.586e-03 bIna.1 0.020668 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIna.2 0.020668 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIna.3 0.020668 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIna.4 0.020668 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 bIna.5 0.020668 0.02418 0.02197 0.01615 1.200e-02 8.701e-03 7.164e-03 6.230e-03 5.586e-03 [,10] [,11] [,12] [,13] [,14] z 6.000e+03 7.000e+03 8.000e+03 9.000e+03 1.000e+04 bI 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 BI 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIa.0 5.150e-03 4.768e-03 4.460e-03 4.205e-03 3.989e-03 bIa.1 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIa.2 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIa.3 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIa.4 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIa.6 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIa.9 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIa.19 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIna.0 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIna.1 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIna.2 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIna.3 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIna.4 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 bIna.5 5.108e-03 4.734e-03 4.433e-03 4.182e-03 3.970e-03 $`N*(2-1i)` [,1] [,2] [,3] [,4] z 100.00000-50.000000i 200.00000-100.00000i 4.000e+02-200.00000i 1000.00000-5.000e+02i bI NA NA NA NA BI 0.02418+ 0.007388i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIa.0 0.03316+ 0.017999i 0.01929+ 0.01843i 5.160e-03+ 0.01815i -0.01155+3.009e-03i bIa.1 0.02352+ 0.004202i 0.01728+ 0.01283i 5.550e-03+ 0.01608i -0.01102+3.119e-03i bIa.2 0.02406+ 0.007842i 0.01720+ 0.01348i 5.480e-03+ 0.01617i -0.01103+3.112e-03i bIa.3 0.02422+ 0.007353i 0.01723+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIa.4 0.02418+ 0.007389i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIa.6 0.02418+ 0.007388i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIa.9 0.02418+ 0.007388i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIa.19 0.02418+ 0.007388i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIna.0 0.02416+ 0.007369i 0.01722+ 0.01343i 5.485e-03+ 0.01616i -0.01103+3.112e-03i bIna.1 0.02418+ 0.007388i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIna.2 0.02418+ 0.007388i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIna.3 0.02418+ 0.007388i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIna.4 0.02418+ 0.007388i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i bIna.5 0.02418+ 0.007388i 0.01722+ 0.01344i 5.484e-03+ 0.01617i -0.01103+3.112e-03i [,5] [,6] [,7] [,8] z 2.000e+03-1.000e+03i 4.000e+03-2.000e+03i 6.000e+03-3.000e+03i 8.000e+03-4.000e+03i bI NA NA NA NA BI 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIa.0 6.220e-03-5.699e-03i -8.587e-04-5.903e-03i -4.380e-03-2.131e-03i -3.659e-03+2.099e-03i bIa.1 6.039e-03-5.648e-03i -8.796e-04-5.840e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIa.2 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIa.3 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIa.4 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIa.6 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIa.9 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIa.19 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIna.0 6.041e-03-5.647e-03i -8.794e-04-5.840e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIna.1 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIna.2 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIna.3 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIna.4 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i bIna.5 6.041e-03-5.647e-03i -8.794e-04-5.841e-03i -4.358e-03-2.102e-03i -3.636e-03+2.097e-03i [,9] [,10] [,11] [,12] z 1.000e+04-5.000e+03i 1.200e+04-6.000e+03i 1.400e+04-7.000e+03i 1.600e+04-8.000e+03i bI NA NA NA NA BI -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIa.0 -2.885e-04+3.762e-03i 2.692e-03+2.149e-03i 3.047e-03-9.416e-04i 8.744e-04-2.852e-03i bIa.1 -2.798e-04+3.747e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIa.2 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIa.3 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIa.4 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIa.6 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIa.9 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIa.19 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIna.0 -2.798e-04+3.747e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIna.1 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIna.2 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIna.3 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIna.4 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i bIna.5 -2.798e-04+3.748e-03i 2.686e-03+2.137e-03i 3.037e-03-9.432e-04i 8.687e-04-2.846e-03i [,13] [,14] z 1.800e+04-9.000e+03i 2.000e+04-1.000e+04i bI NA NA BI -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIa.0 -1.760e-03-2.194e-03i -2.660e-03+2.099e-04i bIa.1 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIa.2 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIa.3 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIa.4 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIa.6 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIa.9 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIa.19 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIna.0 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIna.1 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIna.2 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIna.3 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIna.4 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i bIna.5 -1.758e-03-2.187e-03i -2.654e-03+2.121e-04i $`N*(1+1i)` [,1] [,2] [,3] [,4] z 50.00000+50.000000i 100.00000+100.00000i 2.000e+02+200.00000i 500.00000+5.000e+02i bI NA NA NA NA BI 0.02844- 0.004451i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i bIa.0 0.03753- 0.029020i 0.02023- 0.02676i 2.749e-03- 0.02356i -0.01494-1.409e-03i bIa.1 0.03329+ 0.004173i 0.02186- 0.01505i 5.344e-03- 0.02028i -0.01412-2.084e-03i bIa.2 0.02621- 0.004976i 0.02023- 0.01628i 4.985e-03- 0.02032i -0.01412-2.047e-03i bIa.3 0.02875- 0.004652i 0.02045- 0.01631i 5.001e-03- 0.02034i -0.01413-2.048e-03i bIa.4 0.02843- 0.004409i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i bIa.6 0.02844- 0.004451i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i bIa.9 0.02844- 0.004451i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i bIa.19 0.02844- 0.004451i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i bIna.0 0.02841- 0.004411i 0.02044- 0.01627i 5.006e-03- 0.02033i -0.01412-2.050e-03i bIna.1 0.02844- 0.004450i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i bIna.2 0.02844- 0.004451i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i bIna.3 0.02844- 0.004451i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i bIna.4 0.02844- 0.004451i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i bIna.5 0.02844- 0.004451i 0.02044- 0.01630i 5.001e-03- 0.02033i -0.01413-2.048e-03i [,5] [,6] [,7] [,8] z 1.000e+03+1.000e+03i 2.000e+03+2.000e+03i 3.000e+03+3.000e+03i 4.000e+03+4.000e+03i bI NA NA NA NA BI 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIa.0 8.869e-03+5.821e-03i 1.232e-04+7.500e-03i -5.007e-03+3.527e-03i -4.964e-03-1.868e-03i bIa.1 8.502e-03+5.897e-03i 2.813e-05+7.408e-03i -4.995e-03+3.456e-03i -4.922e-03-1.887e-03i bIa.2 8.506e-03+5.892e-03i 2.928e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIa.3 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIa.4 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIa.6 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIa.9 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIa.19 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIna.0 8.505e-03+5.892e-03i 2.904e-05+7.408e-03i -4.995e-03+3.456e-03i -4.922e-03-1.887e-03i bIna.1 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIna.2 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIna.3 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIna.4 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i bIna.5 8.506e-03+5.892e-03i 2.927e-05+7.408e-03i -4.995e-03+3.457e-03i -4.922e-03-1.887e-03i [,9] [,10] [,11] [,12] z 5.000e+03+5.000e+03i 6.000e+03+6.000e+03i 7.000e+03+7.000e+03i 8.000e+03+8.000e+03i bI NA NA NA NA BI -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIa.0 -1.116e-03-4.611e-03i 2.908e-03-3.210e-03i 3.971e-03+5.550e-04i 1.660e-03+3.363e-03i bIa.1 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.672e-04i 1.644e-03+3.358e-03i bIa.2 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIa.3 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIa.4 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIa.6 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIa.9 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIa.19 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIna.0 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.672e-04i 1.644e-03+3.358e-03i bIna.1 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIna.2 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIna.3 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIna.4 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i bIna.5 -1.087e-03-4.594e-03i 2.909e-03-3.184e-03i 3.955e-03+5.671e-04i 1.644e-03+3.358e-03i [,13] [,14] z 9.000e+03+9.000e+03i 1.000e+04+1.000e+04i bI NA NA BI -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIa.0 -1.742e-03+3.077e-03i -3.343e-03+2.752e-04i bIa.1 -1.746e-03+3.064e-03i -3.336e-03+2.661e-04i bIa.2 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIa.3 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIa.4 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIa.6 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIa.9 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIa.19 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIna.0 -1.746e-03+3.064e-03i -3.336e-03+2.661e-04i bIna.1 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIna.2 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIna.3 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIna.4 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i bIna.5 -1.746e-03+3.064e-03i -3.336e-03+2.662e-04i $`N*(1-2i)` [,1] [,2] [,3] [,4] z 50.00000-100.00000i 100.000000-200.00000i 200.00000-4.000e+02i 500.00000-1.000e+03i bI NA NA NA NA BI 0.02398+ 0.01954i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIa.0 0.01763+ 0.03336i -0.001192+ 0.02665i -0.01687+8.445e-03i 0.01089-4.865e-03i bIa.1 0.02742+ 0.01967i 0.004244+ 0.02423i -0.01519+9.707e-03i 0.01048-5.202e-03i bIa.2 0.02379+ 0.01909i 0.003741+ 0.02382i -0.01516+9.594e-03i 0.01048-5.191e-03i bIa.3 0.02395+ 0.01958i 0.003731+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIa.4 0.02398+ 0.01955i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIa.6 0.02398+ 0.01954i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIa.9 0.02398+ 0.01954i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIa.19 0.02398+ 0.01954i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIna.0 0.02399+ 0.01951i 0.003744+ 0.02385i -0.01516+9.597e-03i 0.01048-5.192e-03i bIna.1 0.02398+ 0.01954i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIna.2 0.02398+ 0.01954i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIna.3 0.02398+ 0.01954i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIna.4 0.02398+ 0.01954i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i bIna.5 0.02398+ 0.01954i 0.003733+ 0.02386i -0.01517+9.595e-03i 0.01048-5.191e-03i [,5] [,6] [,7] [,8] z 1.000e+03-2.000e+03i 2.000e+03-4.000e+03i 3.000e+03-6.000e+03i 4.000e+03-8.000e+03i bI NA NA NA NA BI 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIa.0 1.488e-03-8.304e-03i -5.848e-03+1.179e-03i 2.650e-03+4.087e-03i 2.448e-03-3.435e-03i bIa.1 1.307e-03-8.251e-03i -5.807e-03+1.232e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIa.2 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIa.3 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIa.4 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIa.6 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIa.9 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIa.19 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIna.0 1.308e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIna.1 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIna.2 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIna.3 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIna.4 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i bIna.5 1.309e-03-8.250e-03i -5.807e-03+1.231e-03i 2.668e-03+4.056e-03i 2.425e-03-3.439e-03i [,9] [,10] [,11] [,12] z 5.000e+03-1.000e+04i 6.000e+03-1.200e+04i 7.000e+03-1.400e+04i 8.000e+03-1.600e+04i bI NA NA NA NA BI -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIa.0 -3.662e-03-9.078e-04i 4.577e-04+3.414e-03i 2.784e-03-1.555e-03i -2.310e-03-1.887e-03i bIa.1 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIa.2 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIa.3 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIa.4 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIa.6 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIa.9 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIa.19 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIna.0 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIna.1 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIna.2 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIna.3 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIna.4 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i bIna.5 -3.658e-03-8.914e-04i 4.683e-04+3.406e-03i 2.775e-03-1.561e-03i -2.312e-03-1.879e-03i [,13] [,14] z 9.000e+03-1.800e+04i 1.000e+04-2.000e+04i bI NA NA BI -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIa.0 -8.544e-04+2.679e-03i 2.662e-03-1.802e-04i bIa.1 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIa.2 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIa.3 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIa.4 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIa.6 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIa.9 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIa.19 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIna.0 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIna.1 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIna.2 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIna.3 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIna.4 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i bIna.5 -8.475e-04+2.678e-03i 2.659e-03-1.853e-04i > relE.Iz <- lapply(Iz, function(m) abs(m[,-(1:2)]/m[,"BI"] - 1)) > relE.Iz ## rel.errors : now all go to "zero" nicely $N BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 bIa.9 [1,] 0 1.729716878 9.931757e-01 3.376380e-01 7.824125e-02 1.299227e-02 1.321611e-04 2.316413e-09 [2,] 0 0.650111742 1.728815e-01 2.823748e-02 3.187358e-03 2.595545e-04 6.413491e-07 1.360578e-12 [3,] 0 0.283959942 3.622757e-02 2.895343e-03 1.611348e-04 6.493887e-06 3.952243e-09 1.110223e-15 [4,] 0 0.105001413 5.222478e-03 1.647148e-04 3.634946e-06 5.822695e-08 5.618617e-12 0.000000e+00 [5,] 0 0.051165498 1.261381e-03 1.980063e-05 2.178366e-07 1.740994e-09 4.196643e-14 2.220446e-16 [6,] 0 0.025257382 3.099738e-04 2.427302e-06 1.333213e-08 5.321921e-11 2.220446e-16 0.000000e+00 [7,] 0 0.016766767 1.369806e-04 7.145469e-07 2.615167e-09 6.956880e-12 2.220446e-16 2.220446e-16 [8,] 0 0.012548381 7.683169e-05 3.004729e-07 8.245692e-10 1.644906e-12 0.000000e+00 0.000000e+00 [9,] 0 0.010025920 4.908806e-05 1.535430e-07 3.370366e-10 5.375700e-13 1.110223e-16 1.110223e-16 [10,] 0 0.008347841 3.405000e-05 8.874067e-08 1.623099e-10 2.158274e-13 0.000000e+00 0.000000e+00 [11,] 0 0.007150955 2.499592e-05 5.583157e-08 8.752332e-11 9.992007e-14 2.220446e-16 2.220446e-16 [12,] 0 0.006254240 1.912580e-05 3.737681e-08 5.126632e-11 5.107026e-14 0.000000e+00 0.000000e+00 [13,] 0 0.005557359 1.510455e-05 2.623674e-08 3.198652e-11 2.842171e-14 2.220446e-16 2.220446e-16 [14,] 0 0.005000209 1.223003e-05 1.911831e-08 2.097644e-11 1.687539e-14 2.220446e-16 2.220446e-16 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 bIna.5 [1,] 0.000000e+00 2.310576e-03 2.156993e-05 3.182994e-07 4.953179e-09 5.740075e-12 1.029354e-11 [2,] 2.220446e-16 1.228397e-03 6.628121e-06 6.445612e-08 8.929708e-10 1.574296e-11 3.276268e-13 [3,] 1.110223e-16 6.229749e-04 1.736371e-06 8.906926e-09 6.673040e-11 6.580292e-13 9.436896e-15 [4,] 0.000000e+00 2.500020e-04 2.810109e-07 5.843772e-10 1.783462e-12 5.995204e-15 1.110223e-15 [5,] 2.220446e-16 1.250276e-04 7.032984e-08 7.324519e-11 1.120215e-13 1.110223e-16 0.000000e+00 [6,] 0.000000e+00 6.251029e-05 1.758324e-08 9.158230e-12 6.772360e-15 4.440892e-16 4.440892e-16 [7,] 2.220446e-16 4.167174e-05 7.814306e-09 2.713718e-12 1.665335e-15 3.330669e-16 3.330669e-16 [8,] 0.000000e+00 3.125300e-05 4.395355e-09 1.145084e-12 6.661338e-16 3.330669e-16 3.330669e-16 [9,] 1.110223e-16 2.500197e-05 2.812941e-09 5.865308e-13 4.440892e-16 4.440892e-16 4.440892e-16 [10,] 0.000000e+00 2.083473e-05 1.953387e-09 3.389511e-13 2.220446e-16 2.220446e-16 2.220446e-16 [11,] 2.220446e-16 1.785818e-05 1.435118e-09 2.139400e-13 5.551115e-16 5.551115e-16 5.551115e-16 [12,] 0.000000e+00 1.562580e-05 1.098747e-09 1.428857e-13 2.220446e-16 2.220446e-16 2.220446e-16 [13,] 2.220446e-16 1.388953e-05 8.681360e-10 9.980905e-14 8.881784e-16 8.881784e-16 8.881784e-16 [14,] 2.220446e-16 1.250052e-05 7.031851e-10 7.360779e-14 2.220446e-16 2.220446e-16 2.220446e-16 $`N*(2-1i)` BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0.000000e+00 0.549615545 1.286935e-01 1.864826e-02 1.872731e-03 1.358653e-04 2.670188e-07 [2,] 0.000000e+00 0.247258126 2.798032e-02 1.991414e-03 9.884799e-05 3.555750e-06 1.726080e-09 [3,] 0.000000e+00 0.117382540 6.527627e-03 2.301845e-04 5.679392e-06 1.017153e-07 1.226936e-11 [4,] 0.000000e+00 0.045529024 1.002178e-03 1.405798e-05 1.382492e-07 9.878434e-10 1.891602e-14 [5,] 0.000000e+00 0.022533180 2.471288e-04 1.730080e-06 8.496844e-09 3.033019e-11 7.661947e-17 [6,] 0.000000e+00 0.011209308 6.136003e-05 2.145827e-07 5.266192e-10 9.395909e-13 1.326568e-16 [7,] 0.000000e+00 0.007460196 2.720889e-05 6.341531e-08 1.037331e-10 1.233671e-13 2.220446e-16 [8,] 0.000000e+00 0.005590402 1.528753e-05 2.671865e-08 3.277598e-11 2.934903e-14 0.000000e+00 [9,] 0.000000e+00 0.004470045 9.777319e-06 1.366931e-08 1.341392e-11 9.408727e-15 2.239008e-16 [10,] 0.000000e+00 0.003723774 6.786704e-06 7.906376e-09 6.464947e-12 3.839166e-15 9.885652e-17 [11,] 3.256331e-17 0.003191033 4.984524e-06 4.977098e-09 3.488289e-12 1.901120e-15 2.753417e-16 [12,] 0.000000e+00 0.002791646 3.815342e-06 3.333340e-09 2.044176e-12 9.641540e-16 0.000000e+00 [13,] 0.000000e+00 0.002481113 3.014018e-06 2.340605e-09 1.275702e-12 5.305311e-16 1.806860e-16 [14,] 0.000000e+00 0.002232749 2.440983e-06 1.706006e-09 8.369231e-13 3.900303e-16 1.128621e-16 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 4.027550e-13 2.315344e-16 1.110323e-03 5.487348e-06 4.967000e-08 6.541924e-10 1.129791e-11 [2,] 4.570469e-16 3.388981e-16 5.585421e-04 1.400117e-06 6.481016e-09 4.395196e-11 3.783063e-13 [3,] 3.365239e-16 3.365239e-16 2.795716e-04 3.515007e-07 8.178308e-10 2.800858e-12 1.703316e-14 [4,] 0.000000e+00 0.000000e+00 1.118309e-04 5.627314e-08 5.237527e-11 9.591681e-15 6.255993e-14 [5,] 2.348922e-16 2.348922e-16 5.591003e-05 1.406642e-08 6.427157e-12 1.227949e-13 1.270233e-13 [6,] 1.326568e-16 1.326568e-16 2.795311e-05 3.516390e-09 1.077609e-12 2.689175e-13 2.686837e-13 [7,] 2.220446e-16 2.220446e-16 1.863493e-05 1.562249e-09 3.015127e-13 5.368368e-13 5.369175e-13 [8,] 0.000000e+00 0.000000e+00 1.397601e-05 8.789753e-10 9.243739e-14 1.085740e-14 1.085740e-14 [9,] 2.239008e-16 2.239008e-16 1.118072e-05 5.625301e-10 3.817832e-14 3.230107e-14 3.230107e-14 [10,] 9.885652e-17 9.885652e-17 9.317214e-06 3.893616e-10 1.791189e-12 1.820073e-12 1.820073e-12 [11,] 2.753417e-16 2.753417e-16 7.986153e-06 2.877077e-10 7.366531e-13 7.183948e-13 7.183948e-13 [12,] 0.000000e+00 0.000000e+00 6.987863e-06 2.200026e-10 4.211931e-13 4.179946e-13 4.179946e-13 [13,] 1.806860e-16 1.806860e-16 6.211419e-06 1.740246e-10 9.045460e-13 8.971857e-13 8.971857e-13 [14,] 1.128621e-16 1.128621e-16 5.590266e-06 1.409257e-10 5.224625e-13 5.167145e-13 5.167145e-13 bIna.5 [1,] 2.398410e-13 [2,] 2.463011e-14 [3,] 8.276550e-15 [4,] 6.264844e-14 [5,] 1.270233e-13 [6,] 2.686837e-13 [7,] 5.369175e-13 [8,] 1.085740e-14 [9,] 3.230107e-14 [10,] 1.820073e-12 [11,] 7.183948e-13 [12,] 4.179946e-13 [13,] 8.971857e-13 [14,] 5.167145e-13 $`N*(1+1i)` BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0.00000e+00 0.910000921 3.436047e-01 7.954766e-02 1.271447e-02 1.465328e-03 7.246429e-06 [2,] 0.00000e+00 0.400517416 7.233078e-02 8.179775e-03 6.439976e-04 3.671096e-05 4.469277e-08 [3,] 0.00000e+00 0.187913563 1.659744e-02 9.276238e-04 3.624386e-05 1.027467e-06 3.103181e-10 [4,] 0.00000e+00 0.072351140 2.522578e-03 5.600178e-05 8.713128e-07 9.848248e-09 4.737205e-13 [5,] 0.00000e+00 0.035718368 6.199362e-04 6.865357e-06 5.332801e-08 3.010516e-10 3.384528e-15 [6,] 0.00000e+00 0.017745971 1.536627e-04 8.498630e-07 3.298269e-09 9.304697e-12 2.561076e-17 [7,] 0.00000e+00 0.011805595 6.809987e-05 2.509962e-07 6.492392e-10 1.220922e-12 2.296752e-16 [8,] 3.84104e-17 0.008844817 3.825155e-05 1.057175e-07 2.050646e-10 2.895533e-13 3.352744e-16 [9,] 0.00000e+00 0.007071355 2.446004e-05 5.407473e-08 8.390695e-11 9.434329e-14 2.264991e-16 [10,] 0.00000e+00 0.005890298 1.697644e-05 3.127296e-08 4.043635e-11 3.802756e-14 0.000000e+00 [11,] 0.00000e+00 0.005047298 1.246741e-05 1.968464e-08 2.181531e-11 1.764387e-14 2.686171e-17 [12,] 0.00000e+00 0.004415383 9.542439e-06 1.318259e-08 1.278315e-11 8.927501e-15 1.041743e-16 [13,] 0.00000e+00 0.003924092 7.537912e-06 9.256054e-09 7.978085e-12 4.889289e-15 5.342673e-17 [14,] 0.00000e+00 0.003531183 6.104547e-06 6.746205e-09 5.233381e-12 2.897400e-15 2.745565e-16 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 4.349020e-11 3.479626e-16 1.775971e-03 1.424329e-05 2.137662e-07 4.816189e-09 1.480404e-10 [2,] 3.285662e-14 2.220446e-16 8.858586e-04 3.532878e-06 2.611083e-08 2.840999e-10 4.094619e-12 [3,] 1.180838e-16 1.180838e-16 4.424282e-04 8.809495e-07 3.248595e-09 1.760637e-11 1.294148e-13 [4,] 0.000000e+00 0.000000e+00 1.768541e-04 1.407543e-07 2.075062e-10 4.365673e-13 1.023859e-13 [5,] 5.551115e-16 5.551115e-16 8.840769e-05 3.517240e-08 2.595771e-11 6.941253e-14 4.487538e-14 [6,] 2.561076e-17 2.561076e-17 4.419901e-05 8.791451e-09 3.588821e-12 3.921599e-13 3.916259e-13 [7,] 2.296752e-16 2.296752e-16 2.946493e-05 3.907590e-09 1.672842e-12 7.703857e-13 7.702112e-13 [8,] 3.352744e-16 3.352744e-16 2.209830e-05 2.197491e-09 4.353374e-13 6.780144e-14 6.780144e-14 [9,] 2.264991e-16 2.264991e-16 1.767844e-05 1.405815e-09 4.472421e-13 5.638051e-13 5.638440e-13 [10,] 0.000000e+00 0.000000e+00 1.473193e-05 9.777070e-10 1.165074e-12 1.096660e-12 1.096660e-12 [11,] 2.686171e-17 2.686171e-17 1.262730e-05 7.173913e-10 9.242535e-14 1.672310e-13 1.672310e-13 [12,] 1.041743e-16 1.041743e-16 1.104884e-05 5.483440e-10 9.750052e-13 1.007070e-12 1.007070e-12 [13,] 5.342673e-17 5.342673e-17 9.821166e-06 4.331993e-10 8.352776e-13 8.568766e-13 8.568766e-13 [14,] 2.745565e-16 2.745565e-16 8.839029e-06 3.525726e-10 1.083889e-12 1.073584e-12 1.073584e-12 bIna.5 [1,] 5.877621e-12 [2,] 6.714700e-14 [3,] 1.206096e-14 [4,] 1.036132e-13 [5,] 4.487538e-14 [6,] 3.916259e-13 [7,] 7.702112e-13 [8,] 6.780144e-14 [9,] 5.638440e-13 [10,] 1.096660e-12 [11,] 1.672310e-13 [12,] 1.007070e-12 [13,] 8.568766e-13 [14,] 1.073584e-12 $`N*(1-2i)` BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0.000000e+00 0.491359737 1.114523e-01 1.588582e-02 1.578261e-03 1.135971e-04 2.206636e-07 [2,] 0.000000e+00 0.234386895 2.608227e-02 1.840096e-03 9.081958e-05 3.253438e-06 1.569884e-09 [3,] 0.000000e+00 0.114360193 6.305060e-03 2.213325e-04 5.445079e-06 9.731253e-08 1.170226e-11 [4,] 0.000000e+00 0.045063439 9.884715e-04 1.384021e-05 1.359463e-07 9.705554e-10 1.849620e-14 [5,] 0.000000e+00 0.022418252 2.454374e-04 1.716648e-06 8.425859e-09 3.006399e-11 3.202356e-16 [6,] 0.000000e+00 0.011180758 6.114996e-05 2.137488e-07 5.244161e-10 9.353074e-13 1.320383e-16 [7,] 0.000000e+00 0.007447534 2.714678e-05 6.325095e-08 1.034437e-10 1.230732e-13 2.342507e-16 [8,] 0.000000e+00 0.005583287 1.526136e-05 2.666671e-08 3.270752e-11 2.919461e-14 2.220446e-16 [9,] 0.000000e+00 0.004465495 9.763926e-06 1.364805e-08 1.339117e-11 9.518411e-15 1.119001e-16 [10,] 0.000000e+00 0.003720615 6.778957e-06 7.896127e-09 6.456219e-12 3.761613e-15 2.225932e-16 [11,] 5.935267e-17 0.003188713 4.979646e-06 4.971567e-09 3.484083e-12 1.435469e-15 3.330669e-16 [12,] 0.000000e+00 0.002789870 3.812076e-06 3.330099e-09 2.042238e-12 8.733776e-16 2.491304e-16 [13,] 3.679790e-17 0.002479710 3.011724e-06 2.338582e-09 1.274667e-12 4.297817e-16 3.330669e-16 [14,] 0.000000e+00 0.002231613 2.439311e-06 1.704679e-09 8.363512e-13 2.691882e-16 1.014527e-16 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 3.288132e-13 3.442254e-16 1.131853e-03 5.833371e-06 5.635729e-08 8.104401e-10 1.560314e-11 [2,] 7.240861e-16 5.621535e-16 5.609714e-04 1.420288e-06 6.679014e-09 4.630030e-11 4.057667e-13 [3,] 1.378327e-16 1.378327e-16 2.798130e-04 3.525951e-07 8.233841e-10 2.803185e-12 2.907158e-14 [4,] 2.317763e-16 2.317763e-16 1.118346e-04 5.628871e-08 5.251393e-11 1.359974e-13 6.524024e-14 [5,] 7.691773e-17 7.691773e-17 5.590804e-05 1.406603e-08 6.499784e-12 1.890334e-13 1.857906e-13 [6,] 1.320383e-16 1.320383e-16 2.795225e-05 3.515956e-09 7.369761e-13 8.698650e-14 8.737072e-14 [7,] 2.342507e-16 2.342507e-16 1.863450e-05 1.562862e-09 6.484034e-13 4.091010e-13 4.091010e-13 [8,] 2.220446e-16 2.220446e-16 1.397575e-05 8.791395e-10 5.961174e-13 6.668692e-13 6.668692e-13 [9,] 1.119001e-16 1.119001e-16 1.118055e-05 5.626252e-10 2.394556e-13 2.706816e-13 2.706816e-13 [10,] 2.225932e-16 2.225932e-16 9.317092e-06 3.897018e-10 1.090407e-12 1.087990e-12 1.087990e-12 [11,] 3.330669e-16 3.330669e-16 7.986059e-06 2.845763e-10 2.770800e-12 2.769953e-12 2.769953e-12 [12,] 2.491304e-16 2.491304e-16 6.987790e-06 2.187889e-10 1.696357e-12 1.690057e-12 1.690057e-12 [13,] 3.330669e-16 3.330669e-16 6.211363e-06 1.745732e-10 1.040592e-12 1.039906e-12 1.039906e-12 [14,] 1.014527e-16 1.014527e-16 5.590218e-06 1.379823e-10 2.776524e-12 2.777384e-12 2.777384e-12 bIna.5 [1,] 3.769725e-13 [2,] 1.834785e-14 [3,] 2.751497e-14 [4,] 6.506770e-14 [5,] 1.857906e-13 [6,] 8.737072e-14 [7,] 4.091010e-13 [8,] 6.668692e-13 [9,] 2.706816e-13 [10,] 1.087990e-12 [11,] 2.769953e-12 [12,] 1.690057e-12 [13,] 1.039906e-12 [14,] 2.777384e-12 > ## FIXME - check Iz! > > > ## z / 100 > IzE <- lapply(lapply(z, `/`, 100), besselIexpos, nu = 10, expoS=FALSE) > ## FIXME - check ... seems +- reasonable, notably the bIna.k ones ! > if(FALSE) + print(lapply(IzE, t), digits=4) > relE.IzE <- lapply(IzE, function(m) abs(m[,-(1:2)]/m[,"BI"] - 1)) > relE.IzE ## rel.errors nicely go to "zero" as they should $N BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0 3.519397e+12 3.475404e+14 1.681051e+16 5.193786e+17 1.124327e+19 2.004644e+21 [2,] 0 3.939186e+09 1.925277e+11 4.608633e+12 7.040950e+13 7.524456e+14 3.233337e+16 [3,] 0 6.908979e+06 1.653837e+08 1.939818e+09 1.450707e+10 7.569382e+10 7.613262e+11 [4,] 0 5.780330e+03 5.188844e+04 2.299677e+05 6.508327e+05 1.281423e+06 1.782240e+06 [5,] 0 1.259332e+02 5.071462e+02 1.039942e+03 1.377383e+03 1.274120e+03 3.886422e+02 [6,] 0 1.122523e+01 1.926143e+01 1.798945e+01 1.111280e+01 4.847967e+00 3.332518e-01 [7,] 0 4.337423e+00 4.536043e+00 2.692135e+00 1.072541e+00 3.039184e-01 8.904451e-03 [8,] 0 2.511367e+00 1.866869e+00 8.079595e-01 2.368953e-01 4.962349e-02 7.997430e-04 [9,] 0 1.729717e+00 9.931757e-01 3.376380e-01 7.824125e-02 1.299227e-02 1.321611e-04 [10,] 0 1.307796e+00 6.105594e-01 1.707709e-01 3.270050e-02 4.496622e-03 3.146618e-05 [11,] 0 1.047069e+00 4.114677e-01 9.771787e-02 1.593962e-02 1.870103e-03 9.549084e-06 [12,] 0 8.711375e-01 2.953998e-01 6.094088e-02 8.656912e-03 8.855976e-04 3.444299e-06 [13,] 0 7.448946e-01 2.220678e-01 4.048932e-02 5.093516e-03 4.618921e-04 1.413639e-06 [14,] 0 6.501117e-01 1.728815e-01 2.823748e-02 3.187358e-03 2.595545e-04 6.413491e-07 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 2.209914e+23 1.950524e+30 0.008308242 3.152388e-05 3.285574e-06 9.095978e-08 1.987488e-09 [2,] 3.580477e+17 4.568097e+21 0.008138977 1.357080e-05 5.008166e-06 2.474564e-07 1.072174e-08 [3,] 7.191339e+11 1.934484e+13 0.007491945 5.082710e-05 1.036366e-05 5.828229e-07 1.088614e-08 [4,] 5.550163e+04 8.286678e+02 0.004022820 2.810484e-04 1.318611e-05 1.121324e-06 2.022556e-07 [5,] 1.099122e+00 2.819448e-05 0.001225221 2.461130e-04 1.310889e-05 6.536818e-07 1.951636e-07 [6,] 1.004533e-04 1.336153e-12 0.003715952 3.020411e-06 3.898228e-06 3.919144e-07 2.813116e-08 [7,] 7.540338e-07 4.440892e-16 0.003316550 3.343546e-05 3.620440e-09 5.278546e-08 5.836285e-09 [8,] 2.781896e-08 0.000000e+00 0.002755406 2.846989e-05 3.838347e-07 2.842995e-10 7.243202e-10 [9,] 2.316413e-09 1.110223e-16 0.002310576 2.156993e-05 3.182994e-07 4.953186e-09 5.732970e-12 [10,] 3.157765e-10 0.000000e+00 0.001974881 1.633594e-05 2.279067e-07 4.038696e-09 6.852419e-11 [11,] 5.988909e-11 0.000000e+00 0.001718530 1.262493e-05 1.613210e-07 2.782406e-09 5.521628e-11 [12,] 1.438860e-11 4.440892e-16 0.001518367 9.981392e-06 1.161283e-07 1.876125e-09 3.699874e-11 [13,] 4.129586e-12 3.330669e-16 0.001358559 8.059010e-06 8.553369e-08 1.280627e-09 2.402756e-11 [14,] 1.360467e-12 4.440892e-16 0.001228397 6.628121e-06 6.445612e-08 8.929658e-10 1.573808e-11 bIna.5 [1,] 4.087288e-10 [2,] 1.129768e-09 [3,] 3.851296e-09 [4,] 6.815754e-09 [5,] 5.685244e-09 [6,] 7.908925e-10 [7,] 5.394443e-10 [8,] 8.102075e-11 [9,] 1.028644e-11 [10,] 9.370282e-14 [11,] 9.897638e-13 [12,] 8.033574e-13 [13,] 5.073719e-13 [14,] 3.227418e-13 $`N*(2-1i)` BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0.000000e+00 1.227674e+09 5.367075e+10 1.149044e+12 1.569900e+13 1.500162e+14 5.150653e+15 [2,] 0.000000e+00 2.189252e+06 4.688286e+07 4.917092e+08 3.286852e+09 1.532206e+10 1.227137e+11 [3,] 0.000000e+00 9.087710e+03 9.329887e+04 4.701085e+05 1.508864e+06 3.365758e+06 6.008931e+06 [4,] 3.590425e-17 5.676578e+01 2.022144e+02 3.664591e+02 4.289927e+02 3.506255e+02 8.321669e+01 [5,] 0.000000e+00 7.037319e+00 1.043691e+01 8.547924e+00 4.653547e+00 1.793315e+00 9.648047e-02 [6,] 0.000000e+00 1.916176e+00 1.235443e+00 4.706081e-01 1.220768e-01 2.268064e-02 2.885900e-04 [7,] 0.000000e+00 1.058852e+00 4.317937e-01 1.067006e-01 1.812644e-02 2.215775e-03 1.228966e-05 [8,] 0.000000e+00 7.249884e-01 2.157645e-01 3.942357e-02 4.976836e-03 4.531970e-04 1.400026e-06 [9,] 0.000000e+00 5.496155e-01 1.286935e-01 1.864826e-02 1.872731e-03 1.358653e-04 2.670188e-07 [10,] 0.000000e+00 4.420382e-01 8.528950e-02 1.023861e-02 8.535809e-04 5.146263e-05 6.995562e-08 [11,] 0.000000e+00 3.694680e-01 6.061140e-02 6.210291e-03 4.425677e-04 2.282520e-05 2.273024e-08 [12,] 0.000000e+00 3.172668e-01 4.526503e-02 4.045192e-03 2.517202e-04 1.134250e-05 8.629308e-09 [13,] 0.000000e+00 2.779394e-01 3.508072e-02 2.779756e-03 1.535086e-04 6.141321e-06 3.685467e-09 [14,] 0.000000e+00 2.472581e-01 2.798032e-02 1.991414e-03 9.884799e-05 3.555750e-06 1.726080e-09 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 4.045352e+16 1.697102e+20 0.0081953872 3.027138e-05 5.124386e-06 3.036095e-07 1.976141e-08 [2,] 7.933567e+10 6.923875e+11 0.0077085165 9.190274e-05 1.248813e-05 8.871253e-07 7.329689e-08 [3,] 2.672453e+05 1.823438e+04 0.0061086311 3.141469e-04 2.690945e-05 2.675578e-06 5.249802e-07 [4,] 1.580540e-01 5.926946e-06 0.0043901485 3.549154e-04 3.463496e-05 4.437211e-06 8.887784e-07 [5,] 2.015630e-05 7.459389e-14 0.0043570343 8.285531e-05 5.500862e-06 5.532337e-07 6.273849e-08 [6,] 7.069042e-09 2.233416e-16 0.0026403675 2.944486e-05 5.937304e-07 1.944485e-08 1.029607e-09 [7,] 8.731282e-11 2.220446e-16 0.0018206339 1.447507e-05 2.075810e-07 4.321083e-09 1.213057e-10 [8,] 4.151898e-12 3.149501e-16 0.0013809731 8.436611e-06 9.387360e-08 1.514298e-09 3.206081e-11 [9,] 4.029039e-13 0.000000e+00 0.0011103231 5.487348e-06 4.967000e-08 6.541933e-10 1.130177e-11 [10,] 6.078673e-14 2.220446e-16 0.0009276837 3.843472e-06 2.926015e-08 3.250108e-10 4.746044e-12 [11,] 1.233982e-14 2.456715e-16 0.0007963547 2.838048e-06 1.862251e-08 1.786119e-10 2.255203e-12 [12,] 3.132186e-15 0.000000e+00 0.0006974611 2.179815e-06 1.256039e-08 1.059184e-10 1.171639e-12 [13,] 9.288584e-16 4.440892e-16 0.0006203442 1.725988e-06 8.861887e-09 6.664564e-11 6.582744e-13 [14,] 5.812446e-16 3.330669e-16 0.0005585421 1.400117e-06 6.481047e-09 4.397572e-11 3.897066e-13 bIna.5 [1,] 2.123314e-09 [2,] 1.382112e-08 [3,] 1.018037e-07 [4,] 2.058721e-07 [5,] 8.336056e-09 [6,] 7.483530e-11 [7,] 4.541015e-12 [8,] 8.490161e-13 [9,] 2.459327e-13 [10,] 9.133515e-14 [11,] 4.489181e-14 [12,] 1.599057e-14 [13,] 1.403657e-14 [14,] 9.100914e-15 $`N*(1+1i)` BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0.000000e+00 9.300910e+10 6.494860e+12 2.221304e+14 4.852100e+15 7.425082e+16 6.610966e+18 [2,] 0.000000e+00 1.058821e+08 3.660036e+09 6.193709e+10 6.686810e+11 5.047258e+12 1.079018e+14 [3,] 0.000000e+00 1.984904e+05 3.362669e+06 2.785889e+07 1.469243e+08 5.396244e+08 2.663235e+09 [4,] 0.000000e+00 2.514580e+02 1.604118e+03 4.969991e+03 9.767338e+03 1.327769e+04 8.580004e+03 [5,] 0.000000e+00 1.436099e+01 3.845452e+01 5.305333e+01 4.753183e+01 2.980302e+01 4.168250e+00 [6,] 0.000000e+00 3.364727e+00 3.638295e+00 2.257376e+00 9.431342e-01 2.806647e-01 9.085540e-03 [7,] 0.000000e+00 1.800482e+00 1.203040e+00 4.788284e-01 1.301197e-01 2.535606e-02 3.555437e-04 [8,] 0.000000e+00 1.212743e+00 5.853439e-01 1.713758e-01 3.449658e-02 4.996535e-03 3.890664e-05 [9,] 0.000000e+00 9.100009e-01 3.436047e-01 7.954766e-02 1.271447e-02 1.465328e-03 7.246429e-06 [10,] 3.884466e-17 7.267239e-01 2.252979e-01 4.312910e-02 5.716034e-03 5.469975e-04 1.868884e-06 [11,] 0.000000e+00 6.042741e-01 1.588846e-01 2.592618e-02 2.934736e-03 2.401015e-04 6.004902e-07 [12,] 0.000000e+00 5.168431e-01 1.179713e-01 1.677390e-02 1.656959e-03 1.183879e-04 2.260687e-07 [13,] 0.000000e+00 4.513602e-01 9.101589e-02 1.146614e-02 1.004708e-03 6.371335e-05 9.592457e-08 [14,] 0.000000e+00 4.005174e-01 7.233078e-02 8.179775e-03 6.439976e-04 3.671096e-05 4.469277e-08 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 2.558648e+20 7.084593e+25 0.0083654386 3.950458e-05 2.984807e-06 1.300943e-07 1.376115e-08 [2,] 4.076211e+14 1.653024e+17 0.0083666299 6.053808e-05 5.948854e-06 5.106781e-07 4.931119e-08 [3,] 7.349681e+08 4.501351e+08 0.0083854897 1.919387e-04 2.145235e-05 2.288486e-06 3.408726e-07 [4,] 6.818990e+01 1.909843e+00 0.0089089749 9.118198e-04 1.253502e-04 2.841821e-05 8.340168e-06 [5,] 3.555631e-03 3.575625e-07 0.0082731620 6.010355e-04 8.631373e-05 1.704542e-05 4.494695e-06 [6,] 8.939345e-07 6.864172e-16 0.0044624670 9.914981e-05 5.017928e-06 4.155827e-07 4.563389e-08 [7,] 1.009202e-08 4.528197e-16 0.0029693798 4.059431e-05 1.100706e-06 4.829989e-08 3.005763e-09 [8,] 4.597245e-10 2.304299e-16 0.0022227051 2.240685e-05 4.286639e-07 1.261130e-08 5.184182e-10 [9,] 4.349024e-11 2.169037e-16 0.0017759710 1.424329e-05 2.137662e-07 4.816179e-09 1.480215e-10 [10,] 6.456393e-12 3.855597e-16 0.0014787676 9.858972e-06 1.223546e-07 2.256074e-09 5.595902e-11 [11,] 1.301386e-12 2.409863e-16 0.0012667877 7.229709e-06 7.662772e-08 1.200966e-09 2.514271e-11 [12,] 3.274579e-13 2.753358e-16 0.0011079694 5.528471e-06 5.117209e-08 6.987211e-10 1.268812e-11 [13,] 9.715356e-14 1.300905e-16 0.0009845411 4.364399e-06 3.586723e-08 4.342614e-10 6.969616e-12 [14,] 3.295228e-14 8.609107e-17 0.0008858586 3.532878e-06 2.611083e-08 2.841072e-10 4.100377e-12 bIna.5 [1,] 1.240939e-09 [2,] 6.382676e-09 [3,] 7.188621e-08 [4,] 3.071649e-06 [5,] 1.483613e-06 [6,] 6.127545e-09 [7,] 2.389606e-10 [8,] 2.777311e-11 [9,] 5.855251e-12 [10,] 1.766057e-12 [11,] 6.722656e-13 [12,] 2.839263e-13 [13,] 1.263272e-13 [14,] 6.943264e-14 $`N*(1-2i)` BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0.000000e+00 7.704445e+08 3.403161e+10 7.360108e+11 1.016333e+13 9.828124e+13 3.486855e+15 [2,] 0.000000e+00 9.230356e+05 2.019217e+07 2.159662e+08 1.471809e+09 7.002073e+09 5.897149e+10 [3,] 0.000000e+00 2.120355e+03 2.277536e+04 1.189631e+05 3.935077e+05 9.012509e+05 1.677654e+06 [4,] 5.362166e-17 1.012963e+01 4.028332e+01 7.448794e+01 8.686346e+01 6.987726e+01 1.570144e+01 [5,] 0.000000e+00 3.310152e+00 4.583846e+00 3.614711e+00 1.911177e+00 7.181377e-01 3.693192e-02 [6,] 0.000000e+00 1.394475e+00 8.428459e-01 3.106360e-01 7.880581e-02 1.439265e-02 1.783005e-04 [7,] 0.000000e+00 8.686492e-01 3.373679e-01 8.130328e-02 1.358522e-02 1.640158e-03 8.928172e-06 [8,] 0.000000e+00 6.282400e-01 1.798946e-01 3.222079e-02 4.014814e-03 3.620685e-04 1.102529e-06 [9,] 0.000000e+00 4.913597e-01 1.114523e-01 1.588582e-02 1.578261e-03 1.135971e-04 2.206636e-07 [10,] 0.000000e+00 4.032055e-01 7.572462e-02 8.963646e-03 7.404990e-04 4.434633e-05 5.969319e-08 [11,] 0.000000e+00 3.417641e-01 5.476741e-02 5.543369e-03 3.919210e-04 2.009598e-05 1.984359e-08 [12,] 0.000000e+00 2.965202e-01 4.143792e-02 3.663360e-03 2.263686e-04 1.014801e-05 7.663266e-09 [13,] 0.000000e+00 2.618275e-01 3.243994e-02 2.545712e-03 1.397045e-04 5.563508e-06 3.316608e-09 [14,] 0.000000e+00 2.343869e-01 2.608227e-02 1.840096e-03 9.081958e-05 3.253438e-06 1.569884e-09 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 3.342287e+16 9.596526e+19 0.0085391405 6.167641e-05 2.873674e-06 3.298897e-07 4.192837e-08 [2,] 5.025012e+10 2.507712e+11 0.0090830700 1.576516e-04 1.430845e-05 1.867455e-06 2.798702e-07 [3,] 4.409100e+04 3.818808e+04 0.0115745434 6.976269e-04 1.064197e-04 2.233090e-05 6.353720e-06 [4,] 2.706186e-02 4.630395e-03 0.0233810268 4.611121e-03 1.594389e-03 7.911327e-04 5.056666e-04 [5,] 7.229289e-06 1.626813e-08 0.0074082282 3.308528e-04 3.170520e-05 4.594236e-06 8.848138e-07 [6,] 4.229914e-09 0.000000e+00 0.0030021228 4.377882e-05 1.274945e-06 5.793818e-08 3.611814e-09 [7,] 6.209167e-11 3.647134e-16 0.0019248258 1.723686e-05 2.959397e-07 7.726385e-09 2.748383e-10 [8,] 3.217577e-12 1.154976e-16 0.0014239277 9.294768e-06 1.145432e-07 2.116093e-09 5.268960e-11 [9,] 3.285765e-13 3.330669e-16 0.0011318534 5.833371e-06 5.635728e-08 8.104368e-10 1.560817e-11 [10,] 5.114641e-14 7.419263e-17 0.0009398899 4.007923e-06 3.191637e-08 3.768357e-10 5.937442e-12 [11,] 1.066572e-14 1.408589e-16 0.0008038866 2.925575e-06 1.983794e-08 1.989918e-10 2.669479e-12 [12,] 2.751494e-15 2.379210e-16 0.0007024054 2.230421e-06 1.317718e-08 1.149847e-10 1.329038e-12 [13,] 8.891629e-16 2.558099e-16 0.0006237463 1.757152e-06 9.200647e-09 7.111974e-11 7.308178e-13 [14,] 5.862049e-16 2.663902e-16 0.0005609714 1.420288e-06 6.678989e-09 4.629264e-11 4.237527e-13 bIna.5 [1,] 4.784003e-09 [2,] 5.313432e-08 [3,] 2.261223e-06 [4,] 3.920568e-04 [5,] 2.218207e-07 [6,] 2.853506e-10 [7,] 1.245834e-11 [8,] 1.665446e-12 [9,] 3.856798e-13 [10,] 1.224708e-13 [11,] 5.020103e-14 [12,] 1.610707e-14 [13,] 3.349771e-14 [14,] 2.280978e-14 > ## FIXME check! > > ## z / 40 (<<-- barely no Inf etc) > IzE. <- lapply(lapply(z, `/`, 40), besselIexpos, nu = 10, expoS=FALSE) > if(FALSE) + print(lapply(IzE., t), digits=4) > relE.IzE. <- lapply(IzE., function(m) abs(m[,-(1:2)]/m[,"BI"] - 1)) > relE.IzE. ## rel.errors nicely go to "zero" as they should $N BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0 4.796079e+08 1.865675e+10 3.554590e+11 4.320988e+12 3.671484e+13 9.923161e+14 [2,] 0 1.039942e+06 1.970692e+07 1.830937e+08 1.084410e+09 4.476762e+09 2.798245e+10 [3,] 0 5.780330e+03 5.188844e+04 2.299677e+05 6.508327e+05 1.281423e+06 1.782240e+06 [4,] 0 5.041710e+01 1.547371e+02 2.463394e+02 2.550063e+02 1.849245e+02 3.476297e+01 [5,] 0 6.448682e+00 8.411438e+00 6.114329e+00 2.964276e+00 1.018962e+00 4.373613e-02 [6,] 0 1.729717e+00 9.931757e-01 3.376380e-01 7.824125e-02 1.299227e-02 1.321611e-04 [7,] 0 9.512609e-01 3.463276e-01 7.646999e-02 1.161284e-02 1.269269e-03 5.630240e-06 [8,] 0 6.501117e-01 1.728815e-01 2.823748e-02 3.187358e-03 2.595545e-04 6.413491e-07 [9,] 0 4.924094e-01 1.030619e-01 1.335271e-02 1.199121e-03 7.780176e-05 1.223111e-07 [10,] 0 3.958320e-01 6.828217e-02 7.329759e-03 5.464834e-04 2.946682e-05 3.204214e-08 [11,] 0 3.307469e-01 4.851598e-02 4.445373e-03 2.833191e-04 1.306860e-05 1.041081e-08 [12,] 0 2.839599e-01 3.622757e-02 2.895343e-03 1.611348e-04 6.493887e-06 3.952243e-09 [13,] 0 2.487270e-01 2.807419e-02 1.989493e-03 9.826212e-05 3.515963e-06 1.687915e-09 [14,] 0 2.212486e-01 2.239051e-02 1.425211e-03 6.327152e-05 2.035653e-06 7.905181e-10 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 5.075711e+15 8.438105e+18 0.0080140492 6.145549e-07 6.191692e-06 3.433301e-07 1.621412e-08 [2,] 1.153943e+10 4.884992e+10 0.0070362892 9.214892e-05 1.304250e-05 6.118177e-07 1.937637e-08 [3,] 5.550163e+04 8.286678e+02 0.0040228205 2.810484e-04 1.318611e-05 1.121324e-06 2.022556e-07 [4,] 4.723048e-02 1.244062e-07 0.0025718964 1.509492e-04 1.356327e-05 3.565892e-07 9.390818e-08 [5,] 6.537701e-06 7.549517e-15 0.0035906445 2.831277e-05 1.036060e-06 1.557613e-07 1.465828e-08 [6,] 2.316413e-09 1.110223e-16 0.0023105761 2.156993e-05 3.182994e-07 4.953186e-09 5.732970e-12 [7,] 2.862188e-11 1.110223e-16 0.0016125600 1.119451e-05 1.365003e-07 2.283877e-09 4.557288e-11 [8,] 1.360467e-12 4.440892e-16 0.0012283973 6.628121e-06 6.445612e-08 8.929658e-10 1.573808e-11 [9,] 1.321165e-13 3.330669e-16 0.0009896147 4.340466e-06 3.467228e-08 3.997502e-10 5.961898e-12 [10,] 1.976197e-14 2.220446e-16 0.0008277236 3.051025e-06 2.059240e-08 2.018340e-10 2.565614e-12 [11,] 4.218847e-15 0.000000e+00 0.0007110074 2.257649e-06 1.316718e-08 1.119044e-10 1.233458e-12 [12,] 1.332268e-15 2.220446e-16 0.0006229749 1.736371e-06 8.906893e-09 6.669831e-11 6.260548e-13 [13,] 2.220446e-16 0.000000e+00 0.0005542536 1.376127e-06 6.296545e-09 4.213907e-11 3.725908e-13 [14,] 2.220446e-16 2.220446e-16 0.0004991387 1.117038e-06 4.611241e-09 2.785261e-11 2.052802e-13 bIna.5 [1,] 9.567365e-10 [2,] 1.008934e-08 [3,] 6.815754e-09 [4,] 1.806142e-08 [5,] 1.157183e-09 [6,] 1.028644e-11 [7,] 9.291456e-13 [8,] 3.227418e-13 [9,] 9.992007e-14 [10,] 2.386980e-14 [11,] 4.218847e-15 [12,] 2.264855e-14 [13,] 5.551115e-15 [14,] 1.443290e-14 $`N*(2-1i)` BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0.000000e+00 3.335380e+05 5.655220e+06 4.697275e+07 2.485681e+08 9.162363e+08 4.549977e+09 [2,] 6.259157e-17 2.030655e+03 1.631753e+04 6.450950e+04 1.625845e+05 2.846348e+05 3.107280e+05 [3,] 3.590425e-17 5.676578e+01 2.022144e+02 3.664591e+02 4.289927e+02 3.506255e+02 8.321669e+01 [4,] 4.809246e-17 4.379233e+00 4.930396e+00 3.143797e+00 1.344365e+00 4.086896e-01 1.377003e-02 [5,] 0.000000e+00 1.368478e+00 6.841351e-01 2.051332e-01 4.212139e-02 6.211699e-03 5.000142e-05 [6,] 0.000000e+00 5.496155e-01 1.286935e-01 1.864826e-02 1.872731e-03 1.358653e-04 2.670188e-07 [7,] 0.000000e+00 3.413949e-01 5.210277e-02 4.974107e-03 3.304775e-04 1.589520e-05 1.377301e-08 [8,] 0.000000e+00 2.472581e-01 2.798032e-02 1.991414e-03 9.884799e-05 3.555750e-06 1.726080e-09 [9,] 0.000000e+00 1.937314e-01 1.741786e-02 9.881373e-04 3.914690e-05 1.124640e-06 3.485505e-10 [10,] 0.000000e+00 1.592270e-01 1.187474e-02 5.600274e-04 1.845983e-05 4.414375e-07 9.485349e-11 [11,] 0.000000e+00 1.351434e-01 8.610305e-03 3.474563e-04 9.805830e-06 2.008288e-07 3.166701e-11 [12,] 0.000000e+00 1.173825e-01 6.527627e-03 2.301845e-04 5.679392e-06 1.017153e-07 1.226913e-11 [13,] 2.258384e-17 1.037448e-01 5.118286e-03 1.602690e-04 3.512670e-06 5.589364e-08 5.323468e-12 [14,] 0.000000e+00 9.294453e-02 4.120508e-03 1.160280e-04 2.287519e-06 3.274664e-08 2.524868e-12 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 1.251372e+09 1.751412e+09 0.0073661968 1.436178e-04 1.681827e-05 1.184568e-06 1.394080e-07 [2,] 6.088223e+03 1.024882e+02 0.0052625663 4.055827e-04 3.013507e-05 4.269879e-06 7.889933e-07 [3,] 1.580540e-01 5.926946e-06 0.0043901485 3.549154e-04 3.463496e-05 4.437211e-06 8.887784e-07 [4,] 1.435675e-06 1.994843e-15 0.0038266405 5.943073e-05 2.342246e-06 1.870526e-07 1.851151e-08 [5,] 6.191144e-10 1.383288e-16 0.0021593556 2.011026e-05 3.360454e-07 8.313629e-09 2.958946e-10 [6,] 4.029039e-13 0.000000e+00 0.0011103231 5.487348e-06 4.967000e-08 6.541933e-10 1.130177e-11 [7,] 6.206726e-15 9.768115e-17 0.0007436500 2.476617e-06 1.519751e-08 1.364139e-10 1.604655e-12 [8,] 5.812446e-16 3.330669e-16 0.0005585421 1.400117e-06 6.481047e-09 4.397572e-11 3.897066e-13 [9,] 2.352983e-16 2.352983e-16 0.0004470959 8.980126e-07 3.334116e-09 1.815850e-11 1.204222e-13 [10,] 0.000000e+00 0.000000e+00 0.0003726824 6.242956e-07 1.934175e-09 8.781254e-12 4.668305e-14 [11,] 2.394208e-16 2.394208e-16 0.0003194867 4.589408e-07 1.219712e-09 4.741748e-12 2.450724e-14 [12,] 2.266744e-16 2.266744e-16 0.0002795716 3.515007e-07 8.178403e-10 2.786783e-12 5.118723e-14 [13,] 0.000000e+00 0.000000e+00 0.0002485178 2.777895e-07 5.746876e-10 1.721013e-12 3.368019e-14 [14,] 4.370079e-17 4.370079e-17 0.0002236704 2.250407e-07 4.191056e-10 1.152655e-12 1.937558e-14 bIna.5 [1,] 2.866229e-08 [2,] 1.753130e-07 [3,] 2.058721e-07 [4,] 2.066293e-09 [5,] 1.497840e-11 [6,] 2.459327e-13 [7,] 1.998972e-14 [8,] 9.100914e-15 [9,] 1.433541e-14 [10,] 2.020510e-14 [11,] 2.339177e-14 [12,] 5.749554e-14 [13,] 3.995672e-14 [14,] 1.625620e-14 $`N*(1+1i)` BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0.000000e+00 1.305531e+07 3.592240e+08 4.837742e+09 4.154155e+10 2.491468e+11 3.341010e+12 [2,] 0.000000e+00 3.136602e+04 4.208931e+05 2.759967e+06 1.150878e+07 3.336107e+07 1.013871e+08 [3,] 0.000000e+00 2.514580e+02 1.604118e+03 4.969991e+03 9.767338e+03 1.327769e+04 8.580004e+03 [4,] 0.000000e+00 8.272643e+00 1.636668e+01 1.736028e+01 1.211461e+01 5.954164e+00 5.168157e-01 [5,] 5.958078e-17 2.356884e+00 1.947854e+00 9.448289e-01 3.111720e-01 7.328922e-02 1.495133e-03 [6,] 0.000000e+00 9.100009e-01 3.436047e-01 7.954766e-02 1.271447e-02 1.465328e-03 7.246429e-06 [7,] 0.000000e+00 5.571843e-01 1.361598e-01 2.069087e-02 2.182866e-03 1.665108e-04 3.622349e-07 [8,] 0.000000e+00 4.005174e-01 7.233078e-02 8.179775e-03 6.439976e-04 3.671096e-05 4.469277e-08 [9,] 0.000000e+00 3.123600e-01 4.473099e-02 4.028037e-03 2.529451e-04 1.151035e-05 8.940732e-09 [10,] 0.000000e+00 2.559209e-01 3.036134e-02 2.271308e-03 1.186208e-04 4.491752e-06 2.417945e-09 [11,] 0.000000e+00 2.167188e-01 2.194521e-02 1.404058e-03 6.276301e-05 2.035002e-06 8.036469e-10 [12,] 0.000000e+00 1.879136e-01 1.659744e-02 9.276238e-04 3.624386e-05 1.027467e-06 3.103182e-10 [13,] 0.000000e+00 1.658580e-01 1.298981e-02 6.444945e-04 2.236496e-05 5.632333e-07 1.342921e-10 [14,] 0.000000e+00 1.484306e-01 1.044194e-02 4.657908e-04 1.453762e-05 3.293422e-07 6.356199e-11 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 5.682297e+12 3.021987e+14 0.0083684586 8.302420e-05 8.724634e-06 8.071751e-07 8.370888e-08 [2,] 1.082738e+07 1.492873e+06 0.0084137627 2.934006e-04 3.341496e-05 4.069879e-06 7.541338e-07 [3,] 6.818990e+01 1.909843e+00 0.0089089749 9.118198e-04 1.253502e-04 2.841821e-05 8.340168e-06 [4,] 2.185534e-04 8.154824e-10 0.0069883810 3.355995e-04 3.751425e-05 5.874034e-06 1.194927e-06 [5,] 7.412178e-08 4.787108e-16 0.0035676655 5.991817e-05 2.103873e-06 1.226746e-07 9.936357e-09 [6,] 4.349024e-11 2.169037e-16 0.0017759710 1.424329e-05 2.137662e-07 4.816179e-09 1.480215e-10 [7,] 6.372244e-13 2.424980e-16 0.0011820670 6.293659e-06 6.219041e-08 9.074546e-10 1.764739e-11 [8,] 3.295228e-14 8.609107e-17 0.0008858586 3.532878e-06 2.611083e-08 2.841072e-10 4.100377e-12 [9,] 3.634971e-15 4.751032e-16 0.0007083624 2.258594e-06 1.334045e-08 1.159103e-10 1.335525e-12 [10,] 5.786968e-16 9.644946e-17 0.0005901241 1.567405e-06 7.710863e-09 5.580398e-11 5.523988e-13 [11,] 1.577302e-16 5.257673e-17 0.0005057127 1.151024e-06 4.851965e-09 3.007297e-11 2.530119e-13 [12,] 2.370671e-16 2.237636e-16 0.0004424282 8.809495e-07 3.248607e-09 1.762324e-11 1.414842e-13 [13,] 1.398244e-16 1.398244e-16 0.0003932210 6.958749e-07 2.280654e-09 1.100130e-11 6.857663e-14 [14,] 2.352706e-16 2.352706e-16 0.0003538641 5.635405e-07 1.662045e-09 7.197865e-12 2.264025e-14 bIna.5 [1,] 1.271047e-08 [2,] 1.794082e-07 [3,] 3.071649e-06 [4,] 3.053850e-07 [5,] 1.002816e-09 [6,] 5.855251e-12 [7,] 4.311728e-13 [8,] 6.943264e-14 [9,] 1.688893e-14 [10,] 2.598782e-14 [11,] 9.983678e-15 [12,] 1.597040e-14 [13,] 2.451065e-14 [14,] 3.689918e-14 $`N*(1-2i)` BI bIa.0 bIa.1 bIa.2 bIa.3 bIa.4 bIa.6 [1,] 0.000000e+00 1.182482e+05 2.059817e+06 1.752500e+07 9.488563e+07 3.579771e+08 1.875179e+09 [2,] 0.000000e+00 3.889714e+02 3.319265e+03 1.369558e+04 3.562853e+04 6.387682e+04 7.114880e+04 [3,] 5.362166e-17 1.012963e+01 4.028332e+01 7.448794e+01 8.686346e+01 6.987726e+01 1.570144e+01 [4,] 0.000000e+00 2.484874e+00 2.594034e+00 1.590255e+00 6.610887e-01 1.963869e-01 6.365101e-03 [5,] 0.000000e+00 1.071869e+00 5.067427e-01 1.476569e-01 2.974763e-02 4.324099e-03 3.404797e-05 [6,] 0.000000e+00 4.913597e-01 1.114523e-01 1.588582e-02 1.578261e-03 1.135971e-04 2.206636e-07 [7,] 4.937671e-17 3.175446e-01 4.740857e-02 4.474344e-03 2.950705e-04 1.411510e-05 1.213402e-08 [8,] 0.000000e+00 2.343869e-01 2.608227e-02 1.840096e-03 9.081958e-05 3.253438e-06 1.569884e-09 [9,] 0.000000e+00 1.856971e-01 1.647055e-02 9.277749e-04 3.658707e-05 1.047589e-06 3.231088e-10 [10,] 0.000000e+00 1.537401e-01 1.133579e-02 5.314265e-04 1.744967e-05 4.161129e-07 8.905186e-11 [11,] 0.000000e+00 1.311602e-01 8.275024e-03 3.322117e-04 9.344513e-06 1.909195e-07 3.000068e-11 [12,] 0.000000e+00 1.143602e-01 6.305060e-03 2.213325e-04 5.445079e-06 9.731253e-08 1.170232e-11 [13,] 3.210865e-17 1.013735e-01 4.963080e-03 1.547833e-04 3.383627e-06 5.373882e-08 5.104412e-12 [14,] 0.000000e+00 9.103447e-02 4.008005e-03 1.124500e-04 2.211782e-06 3.160862e-08 2.431256e-12 bIa.9 bIa.19 bIna.0 bIna.1 bIna.2 bIna.3 bIna.4 [1,] 6.543325e+08 7.234954e+08 0.0095128157 2.408393e-04 2.576795e-05 3.665914e-06 6.500149e-07 [2,] 5.753224e+02 6.177752e+02 0.0137102265 1.261673e-03 2.408776e-04 6.666796e-05 2.487239e-05 [3,] 2.706186e-02 4.630395e-03 0.0233810268 4.611121e-03 1.594389e-03 7.911327e-04 5.056666e-04 [4,] 6.305441e-07 7.101522e-11 0.0053595852 1.571214e-04 9.807792e-06 9.502384e-07 1.231195e-07 [5,] 4.109218e-10 4.134774e-16 0.0023417649 2.590050e-05 5.576137e-07 1.847129e-08 8.384356e-10 [6,] 3.285765e-13 3.330669e-16 0.0011318534 5.833371e-06 5.635728e-08 8.104368e-10 1.560817e-11 [7,] 5.459031e-15 2.430145e-16 0.0007497118 2.542579e-06 1.605370e-08 1.498181e-10 1.859446e-12 [8,] 5.862049e-16 2.663902e-16 0.0005609714 1.420288e-06 6.678989e-09 4.629264e-11 4.237527e-13 [9,] 1.152188e-16 1.152188e-16 0.0004482753 9.059971e-07 3.397359e-09 1.877910e-11 1.452978e-13 [10,] 3.380983e-16 3.380983e-16 0.0003733281 6.280145e-07 1.958989e-09 8.973227e-12 1.670561e-14 [11,] 0.000000e+00 0.000000e+00 0.0003198702 4.608778e-07 1.230911e-09 4.811415e-12 1.504786e-14 [12,] 2.220446e-16 2.220446e-16 0.0002798130 3.525951e-07 8.233847e-10 2.803283e-12 2.849767e-14 [13,] 2.939703e-16 2.939703e-16 0.0002486765 2.784472e-07 5.776798e-10 1.746543e-12 3.752843e-14 [14,] 2.307740e-16 2.307740e-16 0.0002237783 2.254555e-07 4.208886e-10 1.267332e-12 1.140517e-13 bIna.5 [1,] 1.479538e-07 [2,] 1.156866e-05 [3,] 3.920568e-04 [4,] 1.980606e-08 [5,] 4.850238e-11 [6,] 3.856798e-13 [7,] 2.492361e-14 [8,] 2.280978e-14 [9,] 1.541359e-14 [10,] 3.857968e-14 [11,] 3.206525e-14 [12,] 2.712932e-14 [13,] 3.317429e-14 [14,] 1.119582e-13 > ## FIXME check! > > > besselKexpos <- function(z, nu, expoS = TRUE) { + drop(cbind(z, + bK = if(is.numeric(z)) besselK(z, nu, expon.scaled=expoS) else NA + , BK = BesselK(z, nu, expon.scaled=expoS) + , bKa.0 = besselKasym(z, nu, k.max=0, expon.scaled=expoS) + , bKa.1 = besselKasym(z, nu, k.max=1, expon.scaled=expoS) + , bKa.2 = besselKasym(z, nu, k.max=2, expon.scaled=expoS) + , bKa.3 = besselKasym(z, nu, k.max=3, expon.scaled=expoS) + , bKa.4 = besselKasym(z, nu, k.max=4, expon.scaled=expoS) + , bKa.6 = besselKasym(z, nu, k.max=6, expon.scaled=expoS) + , bKa.9 = besselKasym(z, nu, k.max=9, expon.scaled=expoS) + , bKa.19= besselKasym(z, nu, k.max=19,expon.scaled=expoS) + , bKna.0 = besselK.nuAsym(z, nu, k.max=0, expon.scaled=expoS) + , bKna.1 = besselK.nuAsym(z, nu, k.max=1, expon.scaled=expoS) + , bKna.2 = besselK.nuAsym(z, nu, k.max=2, expon.scaled=expoS) + , bKna.3 = besselK.nuAsym(z, nu, k.max=3, expon.scaled=expoS) + , bKna.4 = besselK.nuAsym(z, nu, k.max=4, expon.scaled=expoS) + , bKna.5 = besselK.nuAsym(z, nu, k.max=5, expon.scaled=expoS) + )) + } > > cbind(besselKexpos(10000*(1+1i), nu=10)) # looks promising! [,1] z 1.000000e+04+1.000000e+04i bK NA BK 9.751033e-03-4.067527e-03i bKa.0 9.736834e-03-4.033129e-03i bKa.1 9.751058e-03-4.067468e-03i bKa.2 9.751033e-03-4.067527e-03i bKa.3 9.751033e-03-4.067527e-03i bKa.4 9.751033e-03-4.067527e-03i bKa.6 9.751033e-03-4.067527e-03i bKa.9 9.751033e-03-4.067527e-03i bKa.19 9.751033e-03-4.067527e-03i bKna.0 9.751069e-03-4.067613e-03i bKna.1 9.751033e-03-4.067527e-03i bKna.2 9.751033e-03-4.067527e-03i bKna.3 9.751033e-03-4.067527e-03i bKna.4 9.751033e-03-4.067527e-03i bKna.5 9.751033e-03-4.067527e-03i > stopifnot( + all.equal( + BesselK(10000*(1+1i), nu=10, expon.scale=TRUE), + 0.0097510334110568110628-0.0040675270897257763814i, # from Mathematica + tol=1e-15)# Linux F28 64bit: Mean relative Mod difference: 1.642e-16 + ) > > > Kz <- lapply(z, besselKexpos, nu = 10) > print(lapply(Kz, t), digits=4) $N [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] z 50.0000 100.0000 200.00000 500.00000 1.000e+03 2.000e+03 3.000e+03 4.000e+03 5.000e+03 bK 0.4745 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 BK 0.4745 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKa.0 0.1772 0.1253 0.08862 0.05605 3.963e-02 2.802e-02 2.288e-02 1.982e-02 1.772e-02 bKa.1 0.3540 0.1878 0.11072 0.06164 4.161e-02 2.872e-02 2.326e-02 2.006e-02 1.790e-02 bKa.2 0.4405 0.2031 0.11342 0.06191 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKa.3 0.4675 0.2055 0.11363 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKa.4 0.4734 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKa.6 0.4744 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKa.9 0.4745 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKa.19 0.4745 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKna.0 0.4755 0.2060 0.11372 0.06194 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKna.1 0.4744 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKna.2 0.4745 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKna.3 0.4745 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKna.4 0.4745 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 bKna.5 0.4745 0.2058 0.11365 0.06192 4.166e-02 2.873e-02 2.327e-02 2.007e-02 1.790e-02 [,10] [,11] [,12] [,13] [,14] z 6.000e+03 7.000e+03 8.000e+03 9.000e+03 1.000e+04 bK 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 BK 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKa.0 1.618e-02 1.498e-02 1.401e-02 1.321e-02 1.253e-02 bKa.1 1.631e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKa.2 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKa.3 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKa.4 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKa.6 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKa.9 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKa.19 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKna.0 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKna.1 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKna.2 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKna.3 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKna.4 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 bKna.5 1.632e-02 1.509e-02 1.410e-02 1.328e-02 1.260e-02 $`N*(2-1i)` [,1] [,2] [,3] [,4] z 100.0000-50.00000i 200.00000-100.00000i 400.00000-200.00000i 1.000e+03-5.000e+02i bK NA NA NA NA BK 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKa.0 0.1154+ 0.02723i 0.08157+ 0.01926i 0.05768+ 0.01362i 3.648e-02+8.612e-03i bKa.1 0.1560+ 0.06111i 0.09592+ 0.03124i 0.06275+ 0.01785i 3.776e-02+9.683e-03i bKa.2 0.1606+ 0.07171i 0.09674+ 0.03311i 0.06290+ 0.01818i 3.778e-02+9.717e-03i bKa.3 0.1605+ 0.07332i 0.09673+ 0.03325i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKa.4 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKa.6 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKa.9 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKa.19 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKna.0 0.1605+ 0.07361i 0.09677+ 0.03330i 0.06291+ 0.01821i 3.778e-02+9.720e-03i bKna.1 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKna.2 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKna.3 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKna.4 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i bKna.5 0.1604+ 0.07346i 0.09673+ 0.03326i 0.06290+ 0.01820i 3.778e-02+9.717e-03i [,5] [,6] [,7] [,8] z 2.000e+03-1.000e+03i 4.000e+03-2.000e+03i 6.000e+03-3.000e+03i 8.000e+03-4.000e+03i bK NA NA NA NA BK 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKa.0 2.580e-02+6.089e-03i 1.824e-02+4.306e-03i 1.489e-02+3.516e-03i 1.290e-02+3.045e-03i bKa.1 2.625e-02+6.468e-03i 1.840e-02+4.440e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKa.2 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKa.3 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKa.4 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKa.6 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKa.9 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKa.19 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKna.0 2.625e-02+6.475e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKna.1 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKna.2 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKna.3 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKna.4 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i bKna.5 2.625e-02+6.474e-03i 1.840e-02+4.441e-03i 1.498e-02+3.589e-03i 1.295e-02+3.092e-03i [,9] [,10] [,11] [,12] z 1.000e+04-5.000e+03i 1.200e+04-6.000e+03i 1.400e+04-7.000e+03i 1.60e+04-8.000e+03i bK NA NA NA NA BK 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKa.0 1.154e-02+2.723e-03i 1.053e-02+2.486e-03i 9.750e-03+2.302e-03i 9.12e-03+2.153e-03i bKa.1 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKa.2 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKa.3 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKa.4 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKa.6 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKa.9 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKa.19 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKna.0 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKna.1 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKna.2 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKna.3 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKna.4 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i bKna.5 1.158e-02+2.757e-03i 1.056e-02+2.512e-03i 9.774e-03+2.322e-03i 9.14e-03+2.170e-03i [,13] [,14] z 1.800e+04-9.000e+03i 2.000e+04-1.000e+04i bK NA NA BK 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKa.0 8.598e-03+2.030e-03i 8.157e-03+1.926e-03i bKa.1 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKa.2 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKa.3 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKa.4 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKa.6 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKa.9 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKa.19 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKna.0 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKna.1 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKna.2 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKna.3 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKna.4 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i bKna.5 8.615e-03+2.044e-03i 8.172e-03+1.938e-03i $`N*(1+1i)` [,1] [,2] [,3] [,4] z 50.0000+50.00000i 100.00000+100.00000i 200.00000+200.00000i 500.00000+500.00000i bK NA NA NA NA BK 0.1554- 0.19018i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i bKa.0 0.1377- 0.05704i 0.09737- 0.04033i 0.06885- 0.02852i 0.04354- 0.01804i bKa.1 0.1779- 0.15416i 0.11159- 0.07467i 0.07388- 0.04066i 0.04482- 0.02111i bKa.2 0.1640- 0.18773i 0.10913- 0.08060i 0.07344- 0.04171i 0.04477- 0.02121i bKa.3 0.1566- 0.19080i 0.10848- 0.08088i 0.07339- 0.04173i 0.04477- 0.02122i bKa.4 0.1555- 0.19032i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i bKa.6 0.1554- 0.19018i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i bKa.9 0.1554- 0.19018i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i bKa.19 0.1554- 0.19018i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i bKna.0 0.1554- 0.19061i 0.10845- 0.08097i 0.07339- 0.04177i 0.04477- 0.02122i bKna.1 0.1554- 0.19018i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i bKna.2 0.1554- 0.19018i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i bKna.3 0.1554- 0.19018i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i bKna.4 0.1554- 0.19018i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i bKna.5 0.1554- 0.19018i 0.10843- 0.08085i 0.07338- 0.04173i 0.04477- 0.02122i [,5] [,6] [,7] [,8] z 1.000e+03+1.000e+03i 2.000e+03+2.000e+03i 3.000e+03+3.000e+03i 4.000e+03+4.000e+03i bK NA NA NA NA BK 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKa.0 3.079e-02-1.275e-02i 2.177e-02-9.018e-03i 1.778e-02-7.363e-03i 1.540e-02-6.377e-03i bKa.1 3.124e-02-1.384e-02i 2.193e-02-9.402e-03i 1.786e-02-7.572e-03i 1.545e-02-6.513e-03i bKa.2 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKa.3 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKa.4 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKa.6 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKa.9 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKa.19 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKna.0 3.123e-02-1.386e-02i 2.193e-02-9.407e-03i 1.786e-02-7.574e-03i 1.545e-02-6.514e-03i bKna.1 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKna.2 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKna.3 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKna.4 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i bKna.5 3.123e-02-1.386e-02i 2.193e-02-9.406e-03i 1.786e-02-7.574e-03i 1.545e-02-6.513e-03i [,9] [,10] [,11] [,12] z 5.000e+03+5.000e+03i 6.000e+03+6.000e+03i 7.000e+03+7.000e+03i 8.000e+03+8.000e+03i bK NA NA NA NA BK 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKa.0 1.377e-02-5.704e-03i 1.257e-02-5.207e-03i 1.164e-02-4.821e-03i 1.089e-02-4.509e-03i bKa.1 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKa.2 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKa.3 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKa.4 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKa.6 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKa.9 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKa.19 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKna.0 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKna.1 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKna.2 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKna.3 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKna.4 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i bKna.5 1.381e-02-5.801e-03i 1.260e-02-5.281e-03i 1.166e-02-4.879e-03i 1.091e-02-4.557e-03i [,13] [,14] z 9.000e+03+9.000e+03i 1.000e+04+1.000e+04i bK NA NA BK 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKa.0 1.026e-02-4.251e-03i 9.737e-03-4.033e-03i bKa.1 1.028e-02-4.292e-03i 9.751e-03-4.067e-03i bKa.2 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKa.3 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKa.4 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKa.6 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKa.9 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKa.19 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKna.0 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKna.1 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKna.2 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKna.3 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKna.4 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i bKna.5 1.028e-02-4.292e-03i 9.751e-03-4.068e-03i $`N*(1-2i)` [,1] [,2] [,3] [,4] z 50.00000-100.00000i 100.00000-200.00000i 200.00000-400.00000i 500.00000-1.000e+03i bK NA NA NA NA BK 0.08417+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKa.0 0.10083+ 0.06232i 0.07130+ 0.04406i 0.05041+ 0.03116i 0.03188+1.971e-02i bKa.1 0.09608+ 0.11498i 0.06962+ 0.06268i 0.04982+ 0.03774i 0.03173+2.137e-02i bKa.2 0.08532+ 0.11920i 0.06772+ 0.06343i 0.04948+ 0.03787i 0.03170+2.138e-02i bKa.3 0.08412+ 0.11812i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKa.4 0.08416+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKa.6 0.08417+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKa.9 0.08417+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKa.19 0.08417+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKna.0 0.08410+ 0.11811i 0.06760+ 0.06338i 0.04947+ 0.03788i 0.03170+2.139e-02i bKna.1 0.08417+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKna.2 0.08417+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKna.3 0.08417+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKna.4 0.08417+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i bKna.5 0.08417+ 0.11796i 0.06761+ 0.06333i 0.04948+ 0.03786i 0.03170+2.138e-02i [,5] [,6] [,7] [,8] z 1.000e+03-2.000e+03i 2.000e+03-4.000e+03i 3.000e+03-6.000e+03i 4.000e+03-8.000e+03i bK NA NA NA NA BK 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKa.0 2.255e-02+1.393e-02i 1.594e-02+9.853e-03i 1.302e-02+8.045e-03i 1.127e-02+6.967e-03i bKa.1 2.249e-02+1.452e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKa.2 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKa.3 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKa.4 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKa.6 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKa.9 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKa.19 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKna.0 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.159e-03i 1.127e-02+7.041e-03i bKna.1 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKna.2 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKna.3 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKna.4 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i bKna.5 2.249e-02+1.453e-02i 1.592e-02+1.006e-02i 1.301e-02+8.158e-03i 1.127e-02+7.041e-03i [,9] [,10] [,11] [,12] z 5.000e+03-1.000e+04i 6.000e+03-1.200e+04i 7.000e+03-1.400e+04i 8.000e+03-1.600e+04i bK NA NA NA NA BK 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKa.0 1.008e-02+6.232e-03i 9.204e-03+5.689e-03i 8.522e-03+5.267e-03i 7.971e-03+4.926e-03i bKa.1 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.952e-03i bKa.2 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKa.3 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKa.4 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKa.6 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKa.9 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKa.19 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKna.0 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.299e-03i 7.969e-03+4.953e-03i bKna.1 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKna.2 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKna.3 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKna.4 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i bKna.5 1.008e-02+6.284e-03i 9.201e-03+5.729e-03i 8.519e-03+5.298e-03i 7.969e-03+4.953e-03i [,13] [,14] z 9.000e+03-1.800e+04i 1.000e+04-2.000e+04i bK NA NA BK 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKa.0 7.515e-03+4.645e-03i 7.130e-03+4.406e-03i bKa.1 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKa.2 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKa.3 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKa.4 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKa.6 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKa.9 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKa.19 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKna.0 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKna.1 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKna.2 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKna.3 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKna.4 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i bKna.5 7.513e-03+4.667e-03i 7.128e-03+4.425e-03i > ## Relative Errors [Assuming "BK" is accurate also here]: --- here all fine > relE.Kz <- lapply(Kz, function(m) abs(m[,-(1:2)]/m[,"BK"] - 1)) > relE.Kz ## rel.errors nicely go to "zero" as they should $N BK bKa.0 bKa.1 bKa.2 bKa.3 bKa.4 bKa.6 bKa.9 [1,] 0 0.626420664 2.537753e-01 7.164484e-02 1.472908e-02 2.243189e-03 2.017677e-05 3.111574e-10 [2,] 0 0.390964969 8.720875e-02 1.297832e-02 1.379817e-03 1.076061e-04 2.500182e-07 4.977130e-13 [3,] 0 0.220188954 2.572357e-02 1.962336e-03 1.059891e-04 4.180085e-06 2.466928e-09 5.551115e-16 [4,] 0 0.094843256 4.553871e-03 1.409770e-04 3.074064e-06 4.881826e-08 4.653056e-12 0.000000e+00 [5,] 0 0.048627570 1.177870e-03 1.831833e-05 2.003260e-07 1.594136e-09 3.796963e-14 2.220446e-16 [6,] 0 0.024623001 2.995370e-04 2.334678e-06 1.278506e-08 5.092515e-11 2.220446e-16 0.000000e+00 [7,] 0 0.016484828 1.338883e-04 6.962516e-07 2.543127e-09 6.755374e-12 0.000000e+00 0.000000e+00 [8,] 0 0.012389792 7.552715e-05 2.946843e-07 8.074742e-10 1.608935e-12 0.000000e+00 0.000000e+00 [9,] 0 0.009924424 4.842014e-05 1.511720e-07 3.314349e-10 5.286882e-13 2.220446e-16 2.220446e-16 [10,] 0 0.008277358 3.366348e-05 8.759725e-08 1.600594e-10 2.130518e-13 6.661338e-16 6.661338e-16 [11,] 0 0.007099171 2.475251e-05 5.521438e-08 8.648182e-11 9.847678e-14 2.220446e-16 2.220446e-16 [12,] 0 0.006214594 1.896273e-05 3.701502e-08 5.073175e-11 5.018208e-14 2.220446e-16 2.220446e-16 [13,] 0 0.005526033 1.499002e-05 2.601088e-08 3.169043e-11 2.819966e-14 1.110223e-16 1.110223e-16 [14,] 0 0.004974835 1.214654e-05 1.897013e-08 2.080180e-11 1.665335e-14 1.110223e-16 1.110223e-16 bKa.19 bKna.0 bKna.1 bKna.2 bKna.3 bKna.4 bKna.5 [1,] 2.220446e-16 2.278495e-03 2.103956e-05 3.098186e-07 4.968914e-09 1.281486e-11 8.240519e-12 [2,] 1.110223e-16 1.218245e-03 6.516889e-06 6.285462e-08 8.642383e-10 1.513834e-11 3.147482e-13 [3,] 0.000000e+00 6.202905e-04 1.720827e-06 8.785681e-09 6.551171e-11 6.425971e-13 6.661338e-15 [4,] 0.000000e+00 2.495658e-04 2.799855e-07 5.811127e-10 1.772138e-12 6.217249e-15 1.110223e-15 [5,] 2.220446e-16 1.249183e-04 7.020111e-08 7.303957e-11 1.117995e-13 4.440892e-16 0.000000e+00 [6,] 0.000000e+00 6.248295e-05 1.756713e-08 9.145351e-12 7.327472e-15 3.330669e-16 3.330669e-16 [7,] 0.000000e+00 4.165959e-05 7.809532e-09 2.711165e-12 1.221245e-15 2.220446e-16 2.220446e-16 [8,] 0.000000e+00 3.124616e-05 4.393340e-09 1.144418e-12 2.220446e-16 4.440892e-16 4.440892e-16 [9,] 2.220446e-16 2.499760e-05 2.811909e-09 5.857537e-13 0.000000e+00 2.220446e-16 2.220446e-16 [10,] 6.661338e-16 2.083169e-05 1.952791e-09 3.383960e-13 8.881784e-16 6.661338e-16 6.661338e-16 [11,] 2.220446e-16 1.785595e-05 1.434741e-09 2.138290e-13 4.440892e-16 4.440892e-16 4.440892e-16 [12,] 2.220446e-16 1.562409e-05 1.098495e-09 1.429967e-13 2.220446e-16 2.220446e-16 2.220446e-16 [13,] 1.110223e-16 1.388818e-05 8.679605e-10 9.992007e-14 4.440892e-16 4.440892e-16 4.440892e-16 [14,] 1.110223e-16 1.249943e-05 7.030555e-10 7.371881e-14 2.220446e-16 2.220446e-16 2.220446e-16 $`N*(2-1i)` BK bKa.0 bKa.1 bKa.2 bKa.3 bKa.4 bKa.6 [1,] 0.000000e+00 0.365858706 7.440504e-02 1.000765e-02 9.580030e-04 6.713879e-05 1.256083e-07 [2,] 0.000000e+00 0.201731255 2.127457e-02 1.458790e-03 7.069645e-05 2.499469e-06 1.183812e-09 [3,] 0.000000e+00 0.106026453 5.691904e-03 1.970106e-04 4.803024e-06 8.527906e-08 1.016056e-11 [4,] 4.306888e-17 0.043713197 9.487363e-04 1.320956e-05 1.292848e-07 9.205989e-10 1.783490e-14 [5,] 0.000000e+00 0.022079264 2.404494e-04 1.677060e-06 8.216751e-09 2.928014e-11 4.451801e-16 [6,] 0.000000e+00 0.011095831 6.052513e-05 2.112691e-07 5.178669e-10 9.236709e-13 6.794045e-16 [7,] 0.000000e+00 0.007409763 2.696152e-05 6.276078e-08 1.025808e-10 1.223039e-13 4.516208e-16 [8,] 0.000000e+00 0.005562033 1.518317e-05 2.651156e-08 3.250253e-11 2.896326e-14 3.167260e-17 [9,] 0.000000e+00 0.004451889 9.723886e-06 1.358448e-08 1.332416e-11 9.447340e-15 2.330897e-16 [10,] 0.000000e+00 0.003711165 6.755782e-06 7.865468e-09 6.429224e-12 3.835801e-15 3.886309e-17 [11,] 0.000000e+00 0.003181769 4.965051e-06 4.955017e-09 3.471740e-12 1.679327e-15 2.259817e-16 [12,] 0.000000e+00 0.002784554 3.802297e-06 3.320396e-09 2.035739e-12 9.160629e-16 4.491698e-17 [13,] 0.000000e+00 0.002475509 3.004856e-06 2.332525e-09 1.271213e-12 7.675200e-16 2.220446e-16 [14,] 0.000000e+00 0.002228210 2.434304e-06 1.700704e-09 8.341390e-13 2.832522e-16 2.234614e-16 bKa.9 bKa.19 bKna.0 bKna.1 bKna.2 bKna.3 bKna.4 [1,] 1.798906e-13 7.151574e-17 1.102644e-03 5.408384e-06 4.857967e-08 6.348507e-10 1.087647e-11 [2,] 6.115510e-16 6.692157e-16 5.565947e-04 1.389918e-06 6.408815e-09 4.331535e-11 3.863738e-13 [3,] 2.278039e-16 2.278039e-16 2.790830e-04 3.502152e-07 8.132397e-10 2.774404e-12 1.196769e-14 [4,] 4.461728e-16 4.461728e-16 1.117527e-04 5.619071e-08 5.231540e-11 7.155602e-14 1.652080e-15 [5,] 4.484367e-16 4.484367e-16 5.589047e-05 1.405622e-08 6.545854e-12 5.056448e-15 6.223717e-16 [6,] 6.794045e-16 6.794045e-16 2.794822e-05 3.514910e-09 8.182250e-13 1.396004e-15 1.232191e-15 [7,] 4.516208e-16 4.516208e-16 1.863276e-05 1.562296e-09 2.421294e-13 1.143482e-15 1.569668e-15 [8,] 3.167260e-17 3.167260e-17 1.397479e-05 8.788223e-10 1.014238e-13 1.155539e-15 1.132300e-15 [9,] 2.330897e-16 2.330897e-16 1.117994e-05 5.624566e-10 5.256145e-14 2.462001e-16 2.462001e-16 [10,] 3.886309e-17 3.886309e-17 9.316671e-06 3.905991e-10 3.103650e-14 1.411533e-15 1.411533e-15 [11,] 2.259817e-16 2.259817e-16 7.985753e-06 2.869736e-10 1.972619e-14 7.368493e-16 7.368493e-16 [12,] 4.491698e-17 4.491698e-17 6.987557e-06 2.197144e-10 1.383538e-14 2.265421e-15 2.265421e-15 [13,] 2.220446e-16 2.220446e-16 6.211177e-06 1.736039e-10 8.807859e-15 7.249104e-16 7.249104e-16 [14,] 2.234614e-16 2.234614e-16 5.590071e-06 1.406203e-10 6.196284e-15 5.512579e-16 5.512579e-16 bKna.5 [1,] 2.325587e-13 [2,] 3.532564e-15 [3,] 5.553248e-16 [4,] 1.624910e-15 [5,] 6.223717e-16 [6,] 1.232191e-15 [7,] 1.569668e-15 [8,] 1.132300e-15 [9,] 2.462001e-16 [10,] 1.411533e-15 [11,] 7.368493e-16 [12,] 2.265421e-15 [13,] 7.249104e-16 [14,] 5.512579e-16 $`N*(1+1i)` BK bKa.0 bKa.1 bKa.2 bKa.3 bKa.4 bKa.6 [1,] 0.000000e+00 0.546889233 1.729667e-01 3.647857e-02 5.491641e-03 6.061130e-04 2.818361e-06 [2,] 0.000000e+00 0.310544259 5.134538e-02 5.542320e-03 4.234795e-04 2.362392e-05 2.788844e-08 [3,] 7.145023e-17 0.165469621 1.398488e-02 7.636209e-04 2.939270e-05 8.242847e-07 2.451498e-10 [4,] 0.000000e+00 0.068762309 2.355563e-03 5.180929e-05 8.012713e-07 9.017499e-09 4.311760e-13 [5,] 0.000000e+00 0.034821239 5.990628e-04 6.603380e-06 5.113972e-08 2.880742e-10 3.178187e-15 [6,] 0.000000e+00 0.017521693 1.510536e-04 8.334903e-07 3.229889e-09 9.102216e-12 2.991314e-16 [7,] 0.000000e+00 0.011705917 6.732682e-05 2.477621e-07 6.402346e-10 1.203409e-12 2.540658e-16 [8,] 0.000000e+00 0.008788748 3.792542e-05 1.046942e-07 2.029282e-10 2.858334e-13 2.271031e-16 [9,] 0.000000e+00 0.007035471 2.429306e-05 5.365560e-08 8.320684e-11 9.411595e-14 6.682697e-16 [10,] 0.000000e+00 0.005865379 1.687981e-05 3.107083e-08 4.015435e-11 3.752213e-14 3.381741e-16 [11,] 0.000000e+00 0.005028990 1.240655e-05 1.957554e-08 2.168497e-11 1.736327e-14 3.390278e-16 [12,] 0.000000e+00 0.004401366 9.501672e-06 1.311864e-08 1.271587e-11 8.743582e-15 4.492211e-16 [13,] 0.000000e+00 0.003913016 7.509280e-06 9.216128e-09 7.940559e-12 4.743138e-15 3.407287e-16 [14,] 0.000000e+00 0.003522212 6.083674e-06 6.720009e-09 5.210954e-12 2.914492e-15 1.110223e-16 bKa.9 bKa.19 bKna.0 bKna.1 bKna.2 bKna.3 bKna.4 [1,] 1.586604e-11 8.750785e-17 1.758926e-03 1.394491e-05 2.065845e-07 4.587661e-09 1.388415e-10 [2,] 2.007057e-14 3.319600e-16 8.818916e-04 3.499416e-06 2.572766e-08 2.784071e-10 3.993402e-12 [3,] 4.206331e-16 4.206331e-16 4.414552e-04 8.768828e-07 3.225558e-09 1.744360e-11 1.239929e-13 [4,] 2.308867e-16 2.308867e-16 1.766993e-04 1.404960e-07 2.068688e-10 4.478708e-13 8.764292e-16 [5,] 1.856222e-16 1.856222e-16 8.836901e-05 3.514013e-08 2.587778e-11 2.664572e-14 1.667919e-15 [6,] 2.991314e-16 2.991314e-16 4.418934e-05 8.787049e-09 3.234484e-12 2.570715e-15 9.165303e-16 [7,] 2.540658e-16 2.540658e-16 2.946063e-05 3.905654e-09 9.574611e-13 1.758826e-15 1.566052e-15 [8,] 2.271031e-16 2.271031e-16 2.209588e-05 2.197014e-09 4.052973e-13 9.992007e-16 9.992007e-16 [9,] 6.682697e-16 6.682697e-16 1.767690e-05 1.406121e-09 2.068656e-13 3.472115e-16 3.472115e-16 [10,] 3.381741e-16 3.381741e-16 1.473085e-05 9.764871e-10 1.197290e-13 1.346090e-15 1.346090e-15 [11,] 3.390278e-16 3.390278e-16 1.262651e-05 7.174282e-10 7.418032e-14 1.533572e-15 1.533572e-15 [12,] 4.492211e-16 4.492211e-16 1.104824e-05 5.492856e-10 4.942084e-14 1.116826e-15 1.116826e-15 [13,] 3.407287e-16 3.407287e-16 9.820689e-06 4.340059e-10 3.600740e-14 7.001406e-16 7.001406e-16 [14,] 1.110223e-16 1.110223e-16 8.838641e-06 3.515458e-10 2.612034e-14 6.455265e-16 6.455265e-16 bKna.5 [1,] 5.419453e-12 [2,] 7.101207e-14 [3,] 1.512180e-15 [4,] 5.842861e-16 [5,] 1.667919e-15 [6,] 9.165303e-16 [7,] 1.566052e-15 [8,] 9.992007e-16 [9,] 3.472115e-16 [10,] 1.346090e-15 [11,] 1.533572e-15 [12,] 1.116826e-15 [13,] 7.001406e-16 [14,] 6.455265e-16 $`N*(1-2i)` BK bKa.0 bKa.1 bKa.2 bKa.3 bKa.4 bKa.6 [1,] 0.000000e+00 0.400823033 8.469896e-02 1.163064e-02 1.128159e-03 7.980771e-05 1.512552e-07 [2,] 0.000000e+00 0.211707065 2.274156e-02 1.574796e-03 7.680026e-05 2.727526e-06 1.300009e-09 [3,] 0.000000e+00 0.108687371 5.887578e-03 2.047614e-04 5.007335e-06 8.910312e-08 1.064941e-11 [4,] 0.000000e+00 0.044155659 9.617546e-04 1.341606e-05 1.314649e-07 9.369388e-10 1.809898e-14 [5,] 5.443230e-17 0.022191302 2.420978e-04 1.690140e-06 8.285818e-09 2.953894e-11 2.286191e-16 [6,] 0.000000e+00 0.011124020 6.073251e-05 2.120920e-07 5.200401e-10 9.272657e-13 1.557169e-16 [7,] 0.000000e+00 0.007422318 2.702310e-05 6.292369e-08 1.028675e-10 1.222698e-13 9.571555e-17 [8,] 0.000000e+00 0.005569102 1.520918e-05 2.656316e-08 3.257049e-11 2.918883e-14 2.481228e-16 [9,] 0.000000e+00 0.004456417 9.737210e-06 1.360563e-08 1.334652e-11 9.189247e-15 4.440892e-16 [10,] 6.793475e-17 0.003714311 6.763496e-06 7.875673e-09 6.438039e-12 3.456439e-15 4.886219e-16 [11,] 0.000000e+00 0.003184081 4.969910e-06 4.960526e-09 3.475898e-12 2.081122e-15 3.410625e-16 [12,] 0.000000e+00 0.002786324 3.805553e-06 3.323627e-09 2.037638e-12 9.155840e-16 1.570350e-16 [13,] 0.000000e+00 0.002476908 3.007143e-06 2.334542e-09 1.272287e-12 6.474471e-16 3.330669e-16 [14,] 0.000000e+00 0.002229343 2.435971e-06 1.702028e-09 8.348056e-13 2.387858e-16 4.526921e-16 bKa.9 bKa.19 bKna.0 bKna.1 bKna.2 bKna.3 bKna.4 [1,] 2.192789e-13 4.069700e-16 1.127536e-03 5.785111e-06 5.561939e-08 7.957154e-10 1.524126e-11 [2,] 1.093392e-16 2.186784e-16 5.599681e-04 1.414917e-06 6.639902e-09 4.593955e-11 4.225506e-13 [3,] 5.621136e-16 5.621136e-16 2.795669e-04 3.519439e-07 8.210670e-10 2.817653e-12 1.259711e-14 [4,] 1.869670e-16 1.869670e-16 1.117954e-04 5.624742e-08 5.241259e-11 7.208021e-14 1.504350e-16 [5,] 2.286191e-16 2.286191e-16 5.589826e-05 1.406105e-08 6.549560e-12 5.295450e-15 8.354287e-16 [6,] 1.557169e-16 1.557169e-16 2.794981e-05 3.515373e-09 8.197650e-13 8.915845e-16 9.411970e-16 [7,] 9.571555e-17 9.571555e-17 1.863341e-05 1.562419e-09 2.425412e-13 9.691718e-16 9.691718e-16 [8,] 2.481228e-16 2.481228e-16 1.397514e-05 8.788697e-10 1.037813e-13 1.333418e-15 1.333418e-15 [9,] 4.440892e-16 4.440892e-16 1.118016e-05 5.624811e-10 5.271839e-14 4.610597e-16 4.610597e-16 [10,] 4.886219e-16 4.886219e-16 9.316821e-06 3.906155e-10 2.928379e-14 1.553727e-15 1.553727e-15 [11,] 3.410625e-16 3.410625e-16 7.985861e-06 2.869825e-10 1.940509e-14 4.501170e-16 4.501170e-16 [12,] 1.570350e-16 1.570350e-16 6.987639e-06 2.197217e-10 1.343400e-14 6.843933e-16 6.843933e-16 [13,] 3.330669e-16 3.330669e-16 6.211242e-06 1.736078e-10 8.066634e-15 8.328096e-16 8.328096e-16 [14,] 4.526921e-16 4.526921e-16 5.590122e-06 1.406221e-10 7.461022e-15 9.264420e-16 9.264420e-16 bKna.5 [1,] 3.689728e-13 [2,] 4.953183e-15 [3,] 6.719800e-16 [4,] 3.008700e-16 [5,] 8.354287e-16 [6,] 9.411970e-16 [7,] 9.691718e-16 [8,] 1.333418e-15 [9,] 4.610597e-16 [10,] 1.553727e-15 [11,] 4.501170e-16 [12,] 6.843933e-16 [13,] 8.328096e-16 [14,] 9.264420e-16 > ## FIXME: check these relative errors > > ## Open question: here the besselK.nuAsym() converge (to "0" ~ ke-16) for k --> 5; > # ------------- why not for besselI.nuAsym() for the complex case [no problem in real case !!] ??? > > > ## and J() and Y() use imaginary part for scaling by exp( -|abs(Im(z))| ) : > stopifnot(exprs = { + all.eq(BesselJ(20 - 5i, 7, expo=TRUE), exp(-5) * BesselJ(20 - 5i, 7)) + all.eq(BesselY(20 + 5i, 7, expo=TRUE), exp(-5) * BesselY(20 + 5i, 7)) + all.eq(BesselJ(20 + 1i, 8, expo=TRUE), exp(-1) * BesselJ(20 + 1i, 8)) + all.eq(BesselY(20 - 1i, 8, expo=TRUE), exp(-1) * BesselY(20 - 1i, 8)) + }) > > > > > ## check Identity J_nu(i z) = c(nu) * I_nu(z) : > > ## for *integer* nu, it's simple > N <- 100 > set.seed(1) > for(nu in 0:20) { + cat(nu, "") + z <- complex(re = rnorm(N), + im = rnorm(N)) + r <- BesselJ(z * 1i, nu) / BesselI(z, nu) + stopifnot(all.equal(r, rep.int(exp(nu/2*pi*1i), N))) + }; cat("\n") 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 > > nus <- round(sort(rlnorm(20)), 2) > > if(FALSE) { ## Bug ?? + ## For fractional nu, there's a problem (?) : + for(nu in nus) { + cat("nu=", formatC(nu, wid=6),":") + z <- complex(re = rnorm(N), + im = rnorm(N)) + r <- BesselJ(z * 1i, nu) / BesselI(z, nu) + r.Theory <- exp(nu/2*pi*1i) + cat("correct:"); print(table(Ok <- abs(1 - r /r.Theory) < 1e-7)) + cat("log() / (i*pi/2) :", + format(unique(log(signif(r[!Ok], 6)))/(pi/2 * 1i)), + "\n") + } + + }# not for now -- Bug ? > > > ### Replicate some testing "ideas" from zqcbi.f (TOMS 644 test program) > > ## zqcbi is a quick check routine for the complex i bessel function > ## generated by subroutine zbesi. > ## > ## zqcbk generates sequences of i and k bessel functions from > ## zbesi and cbesk and checks the wronskian evaluation > ## > ## I(nu,z)*K(nu+1,z) + I(nu+1,z)*K(nu,z) = 1/z > ## > ## in the right half plane and a modified form > ## > ## I(nu+1,z)*K(nu,zr) - I(nu,z)*K(nu+1,zr) = c/z > ## > ## in the left half plane where zr: = -z and c := exp(nu*sgn*pi*i) with > ## sgn=+1 for Im(z) >= 0 and sgn=-1 for Im(z) < 0. ^^^ > ## ( ||| corrected, MM) > N <- 100 > nS <- 20 > set.seed(257) > > nus. <- unique(sort(c(nus,10*nus))) > ## For exploration nus. <- (1:80)/4 > for(i in seq_along(nus.)) { + nu <- nus.[i] + cat(nu, "") + z <- complex(re = rnorm(N), + im = rnorm(N)) + P <- Re(z) >= 0 + rI <- BesselI( z, nu, nSeq = 1+nS) # -> for (nu, nu+1, ...,nu+nS) + rKp <- BesselK( z[ P], nu, nSeq = 1+nS) + rKm <- BesselK(-z[!P], nu, nSeq = 1+nS) + ## + sgn <- ifelse(Im(z) >= 0, +1, -1) + Izp <- 1 / z [ P] + for(j in 1:nS) { + nu.. <- nu + j-1 + allEQ <- function(x,y) all.equal(x,y, tol= max(1,nu..)*nS*2e-15) + c. <- exp(pi*nu..*sgn*1i) + Izm <- (c./z)[!P] + stopifnot(allEQ(rI[ P,j ]*rKp[,j+1] + rI[ P,j+1]*rKp[,j ], Izp), + allEQ(rI[!P,j+1]*rKm[,j ] - rI[!P,j ]*rKm[,j+1], Izm) ) + } + }; cat("\n") 0.07 0.11 0.19 0.23 0.38 0.55 0.56 0.7 0.86 1.03 1.1 1.43 1.79 1.86 1.89 1.9 1.94 2.24 2.3 2.8 2.91 3.32 3.62 3.8 5.5 5.6 6.28 8.6 10.3 14.3 17.9 18.6 18.9 19.4 22.4 28 29.1 33.2 36.2 62.8 > > > ### Replicate some testing "ideas" from zqcbk.f (TOMS 644 test program) > > ## part 1) in the right half plane ----> see above (I & K) > ## part 2) > ## the analytic continuation formula > ## for H(nu,2,z) in terms of the K function > ## > ## K(nu,z) = c3*H(nu,2,zr) + c4*H(nu,1,zr) Im(z) >= 0 > ## = conjg(K(nu,conjg(z))) Im(z) < 0 > ## > ## in the left half plane where c3=c1*conjg(c2)*c5, c4 = c2*c5 > ## c1=2*cos(pi*nu), c2=exp(pi*nu*i/2), c5 =-pi*i/2 and > ## zr = z*exp(-3*pi*i/2) = z*i > > > ### Replicate some testing "ideas" from zqcbj.f (TOMS 644 test program) > > ## zqcbj is a quick check routine for the complex J bessel function > ## generated by subroutine zbesj. > ## > ## zqcbj generates sequences of J and H bessel functions from zbesj > ## and zbesh and checks the wronskians > ## > ## J(nu,z)*H(nu+1,1,z) - J(nu+1,z)*H(nu,1,z) = 2/(pi*i*z) y >= 0 > ## J(nu,z)*H(nu+1,2,z) - J(nu+1,z)*H(nu,2,z) = -2/(pi*i*z) y < 0 > ## > ## in their respective half planes, y = Im(z) > > N <- 100 > nS <- 20 > set.seed(47) > > for(i in seq_along(nus.)) { + nu <- nus.[i] + cat(nu, "") + z <- complex(re = rnorm(N), + im = rnorm(N)) + P <- Im(z) >= 0 + rJ <- BesselJ( z, nu, nSeq = 1+nS) # -> for (nu, nu+1, ...,nu+nS) + rH1 <- BesselH(1,z[ P], nu, nSeq = 1+nS) + rH2 <- BesselH(2,z[!P], nu, nSeq = 1+nS) + ## + sgn <- ifelse(Im(z) >= 0, +1, -1) + Iz <- 2/(pi*1i*z) + for(j in 1:nS) { + nu.. <- nu + j-1 + allEQ <- function(x,y) all.equal(x,y, tol= max(1,nu..)*nS*1e-15) + stopifnot(allEQ(rJ[ P,j]*rH1[,j+1] - rJ[ P,j+1]*rH1[,j], Iz[ P]), + allEQ(rJ[!P,j]*rH2[,j+1] - rJ[!P,j+1]*rH2[,j], -Iz[!P]) ) + } + }; cat("\n") 0.07 0.11 0.19 0.23 0.38 0.55 0.56 0.7 0.86 1.03 1.1 1.43 1.79 1.86 1.89 1.9 1.94 2.24 2.3 2.8 2.91 3.32 3.62 3.8 5.5 5.6 6.28 8.6 10.3 14.3 17.9 18.6 18.9 19.4 22.4 28 29.1 33.2 36.2 62.8 > > > ### TODO __FIXME__ > > ### Replicate some testing "ideas" from zqcby.f (TOMS 644 test program) > > ## zqcby generates sequences of y bessel functions from zbesy and > ## zbesyh and compares them for a variety of values in the (z,nu) > ## space. zbesyh is an old version of zbesy which computes the y > ## function from the h functions of kinds 1 and 2. > > ###--------> zbesyh() in ../src/zbsubs.c is completely unneeded (otherwise) ! > > > ## "limit z -> 0 does not exist (there are many complex "Inf"s), > ## but for z = real, z >=0 is -Inf > stopifnot(BesselY(0,1) == -Inf,# == besselY(0,1), + is.nan(BesselY(0+0i, 1))) > > ## Subject: bug in Bessel package > ## From: Hiroyuki Kawakatsu <...@gmail.com>, 18 Mar 2015 > > z <- c(0.23+1i, 1.21-1i) > nu <- -1/2 > stopifnot(length(Bz.s <- BesselI(z, nu, expon.scaled=TRUE)) == length(z)) > ## > ## Check that the exp() scaling is correct: > Bzu <- BesselI(z, nu) > stopifnot(abs(Im(sc <- Bz.s / Bzu)) < 1e-15, + all.eq(Re(sc), exp(-abs(Re(z))))) > ## Using nSeq > 1 -- and checking it: > options(warn=2)# warning = error {had warning of incompatible length}: > (Bz.s3 <- BesselI(z, nu, expon.scaled=TRUE, nSeq=3)) [,1] [,2] [,3] [1,] 0.3476759-0.1206017i 0.43668737+0.7306304i -2.0202656+0.6448339i [2,] 0.2589134-0.1662855i 0.05163048-0.2448999i -0.1153078+0.1316307i > stopifnot(length(dim(Bz.s3)) == 2, + dim(Bz.s3) == c(length(z), 3), + all.eq(Bz.s3[,1], Bz.s), + all.eq(Bz.s3[,2], BesselI(z, nu-1, expon.scaled=TRUE)), + all.eq(Bz.s3[,3], BesselI(z, nu-2, expon.scaled=TRUE))) > > #### From: Andrej Gajdoš Date: 18 Sep 2018 > > ## originally, non-complex argument gave non-complex result for K(), Y() -- wrongly: > stopifnot(exprs = { + all.equal(BesselK(-10, 3), + complex(real = -2.72527002565987e-05, + imaginary = -5524.11594151861), + tol = 1e-9) + ## [ tol : not sure about true accuracy] + all.equal(BesselY(-7,2), -0.060526609468272 - 0.60283444017188i, + tol = 1e-9) + }) > > ### very large |x|: > ## inspired from ./Gajdos-BesselK_test.R > > ## larger range > xL <- 10^c(0:8, 5*(2:10), 20*(3:9), 50*(4:6)) > xL <- c(-rev(xL), 0, xL) > stopifnot(!is.unsorted(xL)) > xs <- 1/xL # contains +Inf, fine > > options(warn = 1)# show them as they occur > > ## base:: Bessel functions -- undefined for x < 0 as documented > bR <- cbind(x = xL, + I = besselI(xL, 3),# many NaN, Inf + 29 warnings + J = besselJ(xL, 3),# ... + K = besselK(xL, 3), + Y = besselY(xL, 3)) Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : value out of range in 'bessel_i' Warning in besselI(xL, 3) : NaNs produced Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'bessel_j' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : value out of range in 'J_bessel' Warning in besselJ(xL, 3) : NaNs produced Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : value out of range in 'bessel_k' Warning in besselK(xL, 3) : NaNs produced Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : value out of range in 'bessel_y' Warning in besselY(xL, 3) : NaNs produced > bR x I J K Y [1,] -1e+300 NaN NaN NaN NaN [2,] -1e+250 NaN NaN NaN NaN [3,] -1e+200 NaN NaN NaN NaN [4,] -1e+180 NaN NaN NaN NaN [5,] -1e+160 NaN NaN NaN NaN [6,] -1e+140 NaN NaN NaN NaN [7,] -1e+120 NaN NaN NaN NaN [8,] -1e+100 NaN NaN NaN NaN [9,] -1e+80 NaN NaN NaN NaN [10,] -1e+60 NaN NaN NaN NaN [11,] -1e+50 NaN NaN NaN NaN [12,] -1e+45 NaN NaN NaN NaN [13,] -1e+40 NaN NaN NaN NaN [14,] -1e+35 NaN NaN NaN NaN [15,] -1e+30 NaN NaN NaN NaN [16,] -1e+25 NaN NaN NaN NaN [17,] -1e+20 NaN NaN NaN NaN [18,] -1e+15 NaN NaN NaN NaN [19,] -1e+10 NaN NaN NaN NaN [20,] -1e+08 NaN NaN NaN NaN [21,] -1e+07 NaN NaN NaN NaN [22,] -1e+06 NaN NaN NaN NaN [23,] -1e+05 NaN NaN NaN NaN [24,] -1e+04 NaN NaN NaN NaN [25,] -1e+03 NaN NaN NaN NaN [26,] -1e+02 NaN NaN NaN NaN [27,] -1e+01 NaN NaN NaN NaN [28,] -1e+00 NaN NaN NaN NaN [29,] 0e+00 0.000000e+00 0.000000000 Inf -Inf [30,] 1e+00 2.216842e-02 0.019563354 7.101263e+00 -5.821518e+00 [31,] 1e+01 1.758381e+03 0.058379379 2.725270e-05 -2.513627e-01 [32,] 1e+02 1.026274e+42 0.076284202 4.869863e-45 2.344579e-02 [33,] 1e+03 Inf -0.004827421 0.000000e+00 2.476527e-02 [34,] 1e+04 Inf -0.003644612 0.000000e+00 -7.097801e-03 [35,] 1e+05 Inf -0.001846689 0.000000e+00 -1.719284e-03 [36,] 1e+06 Inf 0.000000000 0.000000e+00 3.310463e-04 [37,] 1e+07 Inf 0.000000000 0.000000e+00 -8.683746e-05 [38,] 1e+08 Inf 0.000000000 0.000000e+00 3.206029e-05 [39,] 1e+10 Inf 0.000000000 0.000000e+00 0.000000e+00 [40,] 1e+15 Inf 0.000000000 0.000000e+00 0.000000e+00 [41,] 1e+20 Inf 0.000000000 0.000000e+00 0.000000e+00 [42,] 1e+25 Inf 0.000000000 0.000000e+00 0.000000e+00 [43,] 1e+30 Inf 0.000000000 0.000000e+00 0.000000e+00 [44,] 1e+35 Inf 0.000000000 0.000000e+00 0.000000e+00 [45,] 1e+40 Inf 0.000000000 0.000000e+00 0.000000e+00 [46,] 1e+45 Inf 0.000000000 0.000000e+00 0.000000e+00 [47,] 1e+50 Inf 0.000000000 0.000000e+00 0.000000e+00 [48,] 1e+60 Inf 0.000000000 0.000000e+00 0.000000e+00 [49,] 1e+80 Inf 0.000000000 0.000000e+00 0.000000e+00 [50,] 1e+100 Inf 0.000000000 0.000000e+00 0.000000e+00 [51,] 1e+120 Inf 0.000000000 0.000000e+00 0.000000e+00 [52,] 1e+140 Inf 0.000000000 0.000000e+00 0.000000e+00 [53,] 1e+160 Inf 0.000000000 0.000000e+00 0.000000e+00 [54,] 1e+180 Inf 0.000000000 0.000000e+00 0.000000e+00 [55,] 1e+200 Inf 0.000000000 0.000000e+00 0.000000e+00 [56,] 1e+250 Inf 0.000000000 0.000000e+00 0.000000e+00 [57,] 1e+300 Inf 0.000000000 0.000000e+00 0.000000e+00 > > > BesselI(-9e9, 1)# now NaN -- FIXME: want 'Inf' (and *no* warning)! Warning in BesselI(-9e+09, 1) : 'zbesi(-9e+09 + 0i, nu=1)' -> ierr=4: |z| or nu too large [1] NaN > > > allBessel <- function(x, nu, ...) { + cbind(x = x, + I = BesselI(x, nu, ...),# many NaN, Inf + 29 warnings + J = BesselJ(x, nu, ...),# ditto + K = BesselK(x, nu, ...),# " + Y = BesselY(x, nu, ...),# " + H1 = BesselH(1, x, nu, ...), + H2 = BesselH(2, x, nu, ...)) + } > > ## This has failed with 'zbesi(-1e+300 + 0i, nu=3)' [Fortran] error ierr = 4 > ## then ... failed with Error in BesselK(xL, 3) : 'zbesk(0 + 0i, nu=3)' unexpected error 'ierr = 1' > ## then ... failed with Error in BesselH(1, xL, 3) : 'zbesh(0 + 0i, nu=3)' unexpected error 'ierr = 1' > BR3 <- allBessel(xL, 3) Warning in BesselI(x, nu, ...) : 'zbesi(-1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+08 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+07 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+06 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(-100000 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(100000 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+06 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+07 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+08 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(100000 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+06 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+07 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+08 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+08 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(-1e+07 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(-1e+06 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(-100000 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(100000 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+06 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+07 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+08 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+08 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+07 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+06 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(-100000 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(100000 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+06 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+07 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+08 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+08 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+07 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+06 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(-100000 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(100000 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+06 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+07 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+08 + 0i, nu=3)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+10 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+15 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+20 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+25 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+30 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+35 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+40 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+45 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+50 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+60 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+80 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+100 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+120 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+140 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+160 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+180 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+200 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+250 + 0i, nu=3)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+300 + 0i, nu=3)' -> ierr=4: |z| or nu too large > options(width = 166) > BR3 x I J K Y H1 H2 [1,] -1e+300+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [2,] -1e+250+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [3,] -1e+200+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [4,] -1e+180+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [5,] -1e+160+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [6,] -1e+140+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [7,] -1e+120+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [8,] -1e+100+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [9,] -1e+80+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [10,] -1e+60+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [11,] -1e+50+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [12,] -1e+45+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [13,] -1e+40+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [14,] -1e+35+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [15,] -1e+30+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [16,] -1e+25+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [17,] -1e+20+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [18,] -1e+15+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [19,] -1e+10+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [20,] -1e+08+0i Inf+Infi 7.306391e-05+0i Inf+ Infi -3.206029e-05+1.461278e-04i -7.306391e-05-3.206029e-05i 2.191917e-04+3.206029e-05i [21,] -1e+07+0i Inf+Infi 2.368992e-04+0i Inf+ Infi 8.683746e-05+4.737984e-04i -2.368992e-04+8.683746e-05i 7.106976e-04-8.683746e-05i [22,] -1e+06+0i Inf+Infi -7.259670e-04+0i Inf+ Infi -3.310463e-04-1.451934e-03i 7.259670e-04-3.310463e-04i -2.177901e-03+3.310463e-04i [23,] -1e+05+0i Inf+Infi 1.846689e-03+0i Inf+ Infi 1.719284e-03+3.693378e-03i -1.846689e-03+1.719284e-03i 5.540066e-03-1.719284e-03i [24,] -1e+04+0i Inf+Infi 3.644612e-03+0i Inf+ Infi 7.097801e-03+7.289224e-03i -3.644612e-03+7.097801e-03i 1.093384e-02-7.097801e-03i [25,] -1e+03+0i Inf+Infi 4.827421e-03+0i Inf+ Infi -2.476527e-02+9.654842e-03i -4.827421e-03-2.476527e-02i 1.448226e-02+2.476527e-02i [26,] -1e+02+0i -1.026274e+42+ 0i -7.628420e-02+0i -4.869863e-45-3.224135e+42i -2.344579e-02-1.525684e-01i 7.628420e-02-2.344579e-02i -2.288526e-01+2.344579e-02i [27,] -1e+01+0i -1.758381e+03+ 0i -5.837938e-02+0i -2.725270e-05-5.524116e+03i 2.513627e-01-1.167588e-01i 5.837938e-02+2.513627e-01i -1.751381e-01-2.513627e-01i [28,] -1e+00+0i -2.216842e-02+ 0i -1.956335e-02+0i -7.101263e+00-6.964416e-02i 5.821518e+00-3.912671e-02i 1.956335e-02+5.821518e+00i -5.869006e-02-5.821518e+00i [29,] 0e+00+0i 0.000000e+00+ 0i 0.000000e+00+0i 0.000000e+00+0.000000e+00i Inf+ NaNi Inf+ Infi Inf+ Infi [30,] 1e+00+0i 2.216842e-02+ 0i 1.956335e-02+0i 7.101263e+00+0.000000e+00i -5.821518e+00-3.781697e-16i 1.956335e-02-5.821518e+00i 1.956335e-02+5.821518e+00i [31,] 1e+01+0i 1.758381e+03+ 0i 5.837938e-02+0i 2.725270e-05+0.000000e+00i -2.513627e-01-1.040834e-16i 5.837938e-02-2.513627e-01i 5.837938e-02+2.513627e-01i [32,] 1e+02+0i 1.026274e+42+ 0i 7.628420e-02+0i 4.869863e-45+0.000000e+00i 2.344579e-02+2.775558e-17i 7.628420e-02+2.344579e-02i 7.628420e-02-2.344579e-02i [33,] 1e+03+0i Inf+Infi -4.827421e-03+0i 0.000000e+00+0.000000e+00i 2.476527e-02+3.469447e-18i -4.827421e-03+2.476527e-02i -4.827421e-03-2.476527e-02i [34,] 1e+04+0i Inf+Infi -3.644612e-03+0i 0.000000e+00+0.000000e+00i -7.097801e-03-8.673617e-19i -3.644612e-03-7.097801e-03i -3.644612e-03+7.097801e-03i [35,] 1e+05+0i Inf+Infi -1.846689e-03+0i 0.000000e+00+0.000000e+00i -1.719284e-03-1.517883e-18i -1.846689e-03-1.719284e-03i -1.846689e-03+1.719284e-03i [36,] 1e+06+0i Inf+Infi 7.259670e-04+0i 0.000000e+00+0.000000e+00i 3.310463e-04-2.168404e-19i 7.259670e-04+3.310463e-04i 7.259670e-04-3.310463e-04i [37,] 1e+07+0i Inf+Infi -2.368992e-04+0i 0.000000e+00+0.000000e+00i -8.683746e-05+0.000000e+00i -2.368992e-04-8.683746e-05i -2.368992e-04+8.683746e-05i [38,] 1e+08+0i Inf+Infi -7.306391e-05+0i 0.000000e+00+0.000000e+00i 3.206029e-05-2.710505e-20i -7.306391e-05+3.206029e-05i -7.306391e-05-3.206029e-05i [39,] 1e+10+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [40,] 1e+15+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [41,] 1e+20+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [42,] 1e+25+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [43,] 1e+30+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [44,] 1e+35+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [45,] 1e+40+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [46,] 1e+45+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [47,] 1e+50+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [48,] 1e+60+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [49,] 1e+80+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [50,] 1e+100+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [51,] 1e+120+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [52,] 1e+140+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [53,] 1e+160+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [54,] 1e+180+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [55,] 1e+200+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [56,] 1e+250+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [57,] 1e+300+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i > > (BR0 <- allBessel(xL, 0)) Warning in BesselI(x, nu, ...) : 'zbesi(-1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+08 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+07 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+06 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(-100000 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(100000 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+06 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+07 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+08 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(100000 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+06 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+07 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+08 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+08 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(-1e+07 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(-1e+06 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(-100000 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(100000 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+06 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+07 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+08 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+08 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+07 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+06 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(-100000 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(100000 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+06 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+07 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+08 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+08 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+07 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+06 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(-100000 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(100000 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+06 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+07 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+08 + 0i, nu=0)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+10 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+15 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+20 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+25 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+30 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+35 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+40 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+45 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+50 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+60 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+80 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+100 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+120 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+140 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+160 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+180 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+200 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+250 + 0i, nu=0)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+300 + 0i, nu=0)' -> ierr=4: |z| or nu too large x I J K Y H1 H2 [1,] -1e+300+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [2,] -1e+250+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [3,] -1e+200+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [4,] -1e+180+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [5,] -1e+160+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [6,] -1e+140+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [7,] -1e+120+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [8,] -1e+100+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [9,] -1e+80+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [10,] -1e+60+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [11,] -1e+50+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [12,] -1e+45+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [13,] -1e+40+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [14,] -1e+35+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [15,] -1e+30+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [16,] -1e+25+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [17,] -1e+20+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [18,] -1e+15+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [19,] -1e+10+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [20,] -1e+08+0i Inf+Infi 3.206030e-05+0i Inf+ Infi 7.306391e-05+6.412059e-05i -3.206030e-05+7.306391e-05i 9.618089e-05-7.306391e-05i [21,] -1e+07+0i Inf+Infi -8.683735e-05+0i Inf+ Infi 2.368992e-04-1.736747e-04i 8.683735e-05+2.368992e-04i -2.605120e-04-2.368992e-04i [22,] -1e+06+0i Inf+Infi 3.310430e-04+0i Inf+ Infi -7.259685e-04+6.620860e-04i -3.310430e-04-7.259685e-04i 9.931290e-04+7.259685e-04i [23,] -1e+05+0i Inf+Infi -1.719201e-03+0i Inf+ Infi 1.846766e-03-3.438402e-03i 1.719201e-03+1.846766e-03i -5.157603e-03-1.846766e-03i [24,] -1e+04+0i Inf+Infi -7.096160e-03+0i Inf+ Infi 3.647806e-03-1.419232e-02i 7.096160e-03+3.647806e-03i -2.128848e-02-3.647806e-03i [25,] -1e+03+0i Inf+Infi 2.478669e-02+0i Inf+ Infi 4.715918e-03+4.957337e-02i -2.478669e-02+4.715918e-03i 7.436006e-02-4.715918e-03i [26,] -1e+02+0i 1.073752e+42+ 0i 1.998585e-02+0i 4.656628e-45-3.373290e+42i -7.724431e-02+3.997170e-02i -1.998585e-02-7.724431e-02i 5.995755e-02+7.724431e-02i [27,] -1e+01+0i 2.815717e+03+ 0i -2.459358e-01+0i 1.778006e-05-8.845835e+03i 5.567117e-02-4.918715e-01i 2.459358e-01+5.567117e-02i -7.378073e-01-5.567117e-02i [28,] -1e+00+0i 1.266066e+00+ 0i 7.651977e-01+0i 4.210244e-01-3.977463e+00i 8.825696e-02+1.530395e+00i -7.651977e-01+8.825696e-02i 2.295593e+00-8.825696e-02i [29,] 0e+00+0i 1.000000e+00+ 0i 1.000000e+00+0i 0.000000e+00+0.000000e+00i Inf+ NaNi Inf+ Infi Inf+ Infi [30,] 1e+00+0i 1.266066e+00+ 0i 7.651977e-01+0i 4.210244e-01+0.000000e+00i 8.825696e-02+2.220446e-16i 7.651977e-01+8.825696e-02i 7.651977e-01-8.825696e-02i [31,] 1e+01+0i 2.815717e+03+ 0i -2.459358e-01+0i 1.778006e-05+0.000000e+00i 5.567117e-02+1.110223e-16i -2.459358e-01+5.567117e-02i -2.459358e-01-5.567117e-02i [32,] 1e+02+0i 1.073752e+42+ 0i 1.998585e-02+0i 4.656628e-45+0.000000e+00i -7.724431e-02+3.469447e-18i 1.998585e-02-7.724431e-02i 1.998585e-02+7.724431e-02i [33,] 1e+03+0i Inf+Infi 2.478669e-02+0i 0.000000e+00+0.000000e+00i 4.715918e-03-3.469447e-18i 2.478669e-02+4.715918e-03i 2.478669e-02-4.715918e-03i [34,] 1e+04+0i Inf+Infi -7.096160e-03+0i 0.000000e+00+0.000000e+00i 3.647806e-03-8.673617e-19i -7.096160e-03+3.647806e-03i -7.096160e-03-3.647806e-03i [35,] 1e+05+0i Inf+Infi -1.719201e-03+0i 0.000000e+00+0.000000e+00i 1.846766e-03-1.084202e-18i -1.719201e-03+1.846766e-03i -1.719201e-03-1.846766e-03i [36,] 1e+06+0i Inf+Infi 3.310430e-04+0i 0.000000e+00+0.000000e+00i -7.259685e-04+0.000000e+00i 3.310430e-04-7.259685e-04i 3.310430e-04+7.259685e-04i [37,] 1e+07+0i Inf+Infi -8.683735e-05+0i 0.000000e+00+0.000000e+00i 2.368992e-04-1.355253e-20i -8.683735e-05+2.368992e-04i -8.683735e-05-2.368992e-04i [38,] 1e+08+0i Inf+Infi 3.206030e-05+0i 0.000000e+00+0.000000e+00i 7.306391e-05+1.355253e-20i 3.206030e-05+7.306391e-05i 3.206030e-05-7.306391e-05i [39,] 1e+10+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [40,] 1e+15+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [41,] 1e+20+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [42,] 1e+25+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [43,] 1e+30+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [44,] 1e+35+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [45,] 1e+40+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [46,] 1e+45+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [47,] 1e+50+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [48,] 1e+60+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [49,] 1e+80+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [50,] 1e+100+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [51,] 1e+120+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [52,] 1e+140+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [53,] 1e+160+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [54,] 1e+180+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [55,] 1e+200+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [56,] 1e+250+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [57,] 1e+300+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i > (BR1 <- allBessel(xL, 1)) Warning in BesselI(x, nu, ...) : 'zbesi(-1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(-1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselI(x, nu, ...) : 'zbesi(1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+08 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+07 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(-1e+06 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(-100000 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(100000 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+06 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+07 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+08 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselJ(x, nu, ...) : 'zbesj(1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselJ(x, nu, ...) : 'zbesj(1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(-1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(100000 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+06 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+07 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+08 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselK(x, nu, ...) : 'zbesk(1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselK(x, nu, ...) : 'zbesk(1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(-1e+08 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(-1e+07 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(-1e+06 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(-100000 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(100000 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+06 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+07 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+08 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselY(x, nu, ...) : 'zbesy(1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselY(x, nu, ...) : 'zbesy(1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+08 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+07 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(-1e+06 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(-100000 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(100000 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+06 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+07 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+08 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(1, x, nu, ...) : 'zbesh(1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+08 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+07 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(-1e+06 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(-100000 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(100000 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+06 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+07 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+08 + 0i, nu=1)' large arguments -> precision loss (of at least half machine accuracy) Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+10 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+15 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+20 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+25 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+30 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+35 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+40 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+45 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+50 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+60 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+80 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+100 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+120 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+140 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+160 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+180 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+200 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+250 + 0i, nu=1)' -> ierr=4: |z| or nu too large Warning in BesselH(2, x, nu, ...) : 'zbesh(1e+300 + 0i, nu=1)' -> ierr=4: |z| or nu too large x I J K Y H1 H2 [1,] -1e+300+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [2,] -1e+250+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [3,] -1e+200+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [4,] -1e+180+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [5,] -1e+160+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [6,] -1e+140+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [7,] -1e+120+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [8,] -1e+100+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [9,] -1e+80+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [10,] -1e+60+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [11,] -1e+50+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [12,] -1e+45+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [13,] -1e+40+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [14,] -1e+35+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [15,] -1e+30+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [16,] -1e+25+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [17,] -1e+20+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [18,] -1e+15+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [19,] -1e+10+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [20,] -1e+08+0i Inf+Infi -7.306391e-05+0i Inf+ Infi 3.206029e-05-1.461278e-04i 7.306391e-05+3.206029e-05i -2.191917e-04-3.206029e-05i [21,] -1e+07+0i Inf+Infi -2.368992e-04+0i Inf+ Infi -8.683736e-05-4.737985e-04i 2.368992e-04-8.683736e-05i -7.106977e-04+8.683736e-05i [22,] -1e+06+0i Inf+Infi 7.259684e-04+0i Inf+ Infi 3.310434e-04+1.451937e-03i -7.259684e-04+3.310434e-04i 2.177905e-03-3.310434e-04i [23,] -1e+05+0i Inf+Infi -1.846758e-03+0i Inf+ Infi -1.719210e-03-3.693515e-03i 1.846758e-03-1.719210e-03i -5.540273e-03+1.719210e-03i [24,] -1e+04+0i Inf+Infi -3.647451e-03+0i Inf+ Infi -7.096343e-03-7.294902e-03i 3.647451e-03-7.096343e-03i -1.094235e-02+7.096343e-03i [25,] -1e+03+0i Inf+Infi -4.728312e-03+0i Inf+ Infi 2.478433e-02-9.456624e-03i 4.728312e-03+2.478433e-02i -1.418494e-02-2.478433e-02i [26,] -1e+02+0i -1.068369e+42+ 0i 7.714535e-02+0i -4.679854e-45-3.356381e+42i 2.037231e-02+1.542907e-01i -7.714535e-02+2.037231e-02i 2.314361e-01-2.037231e-02i [27,] -1e+01+0i -2.670988e+03+ 0i -4.347275e-02+0i -1.864877e-05-8.391157e+03i -2.490154e-01-8.694549e-02i 4.347275e-02-2.490154e-01i -1.304182e-01+2.490154e-01i [28,] -1e+00+0i -5.651591e-01+ 0i -4.400506e-01+0i -6.019072e-01-1.775500e+00i 7.812128e-01-8.801012e-01i 4.400506e-01+7.812128e-01i -1.320152e+00-7.812128e-01i [29,] 0e+00+0i 0.000000e+00+ 0i 0.000000e+00+0i 0.000000e+00+0.000000e+00i Inf+ NaNi Inf+ Infi Inf+ Infi [30,] 1e+00+0i 5.651591e-01+ 0i 4.400506e-01+0i 6.019072e-01+0.000000e+00i -7.812128e-01+5.551115e-17i 4.400506e-01-7.812128e-01i 4.400506e-01+7.812128e-01i [31,] 1e+01+0i 2.670988e+03+ 0i 4.347275e-02+0i 1.864877e-05+0.000000e+00i 2.490154e-01+6.938894e-17i 4.347275e-02+2.490154e-01i 4.347275e-02-2.490154e-01i [32,] 1e+02+0i 1.068369e+42+ 0i -7.714535e-02+0i 4.679854e-45+0.000000e+00i -2.037231e-02+0.000000e+00i -7.714535e-02-2.037231e-02i -7.714535e-02+2.037231e-02i [33,] 1e+03+0i Inf+Infi 4.728312e-03+0i 0.000000e+00+0.000000e+00i -2.478433e-02-2.602085e-18i 4.728312e-03-2.478433e-02i 4.728312e-03+2.478433e-02i [34,] 1e+04+0i Inf+Infi 3.647451e-03+0i 0.000000e+00+0.000000e+00i 7.096343e-03+1.301043e-18i 3.647451e-03+7.096343e-03i 3.647451e-03-7.096343e-03i [35,] 1e+05+0i Inf+Infi 1.846758e-03+0i 0.000000e+00+0.000000e+00i 1.719210e-03+1.517883e-18i 1.846758e-03+1.719210e-03i 1.846758e-03-1.719210e-03i [36,] 1e+06+0i Inf+Infi -7.259684e-04+0i 0.000000e+00+0.000000e+00i -3.310434e-04+2.168404e-19i -7.259684e-04-3.310434e-04i -7.259684e-04+3.310434e-04i [37,] 1e+07+0i Inf+Infi 2.368992e-04+0i 0.000000e+00+0.000000e+00i 8.683736e-05-2.710505e-20i 2.368992e-04+8.683736e-05i 2.368992e-04-8.683736e-05i [38,] 1e+08+0i Inf+Infi 7.306391e-05+0i 0.000000e+00+0.000000e+00i -3.206029e-05+4.065758e-20i 7.306391e-05-3.206029e-05i 7.306391e-05+3.206029e-05i [39,] 1e+10+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [40,] 1e+15+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [41,] 1e+20+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [42,] 1e+25+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [43,] 1e+30+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [44,] 1e+35+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [45,] 1e+40+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [46,] 1e+45+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [47,] 1e+50+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [48,] 1e+60+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [49,] 1e+80+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [50,] 1e+100+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [51,] 1e+120+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [52,] 1e+140+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [53,] 1e+160+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [54,] 1e+180+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [55,] 1e+200+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [56,] 1e+250+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i [57,] 1e+300+0i NaN+ 0i NaN+0i NaN+0.000000e+00i NaN+ NaNi NaN+0.000000e+00i NaN+0.000000e+00i > > try(## Fails: NA/NaN/Inf in foreign function call [Inf !] + BRs1 <- allBessel(xs, 1) + ) Error in BesselI(x, nu, ...) : NA/NaN/Inf in foreign function call (arg 1) > > xs. <- sort(xs[is.finite(xs)]) > > (BRs0 <- allBessel(xs., 0)) x I J K Y H1 H2 [1,] -1e+00+0i 1.266066+0i 0.7651977+0i 0.4210244-3.977463i 0.08825696+1.530395e+00i -0.7651977+ 0.08825696i 2.2955931- 0.08825696i [2,] -1e-01+0i 1.002502+0i 0.9975016+0i 2.4270690-3.149452i -1.53423865+1.995003e+00i -0.9975016- 1.53423865i 2.9925047+ 1.53423865i [3,] -1e-02+0i 1.000025+0i 0.9999750+0i 4.7212447-3.141671i -3.00545564+1.999950e+00i -0.9999750- 3.00545564i 2.9999250+ 3.00545564i [4,] -1e-03+0i 1.000000+0i 0.9999998+0i 7.0236888-3.141593i -4.47141661+2.000000e+00i -0.9999998- 4.47141661i 2.9999993+ 4.47141661i [5,] -1e-04+0i 1.000000+0i 1.0000000+0i 9.3262719-3.141593i -5.93728907+2.000000e+00i -1.0000000- 5.93728907i 3.0000000+ 5.93728907i [6,] -1e-05+0i 1.000000+0i 1.0000000+0i 11.6288570-3.141593i -7.40316028+2.000000e+00i -1.0000000- 7.40316028i 3.0000000+ 7.40316028i [7,] -1e-06+0i 1.000000+0i 1.0000000+0i 13.9314421-3.141593i -8.86903148+2.000000e+00i -1.0000000- 8.86903148i 3.0000000+ 8.86903148i [8,] -1e-07+0i 1.000000+0i 1.0000000+0i 16.2340272-3.141593i -10.33490268+2.000000e+00i -1.0000000- 10.33490268i 3.0000000+ 10.33490268i [9,] -1e-08+0i 1.000000+0i 1.0000000+0i 18.5366123-3.141593i -11.80077388+2.000000e+00i -1.0000000- 11.80077388i 3.0000000+ 11.80077388i [10,] -1e-10+0i 1.000000+0i 1.0000000+0i 23.1417824-3.141593i -14.73251627+2.000000e+00i -1.0000000- 14.73251627i 3.0000000+ 14.73251627i [11,] -1e-15+0i 1.000000+0i 1.0000000+0i 34.6547079-3.141593i -22.06187226+2.000000e+00i -1.0000000- 22.06187226i 3.0000000+ 22.06187226i [12,] -1e-20+0i 1.000000+0i 1.0000000+0i 46.1676334-3.141593i -29.39122825+2.000000e+00i -1.0000000- 29.39122825i 3.0000000+ 29.39122825i [13,] -1e-25+0i 1.000000+0i 1.0000000+0i 57.6805588-3.141593i -36.72058424+2.000000e+00i -1.0000000- 36.72058424i 3.0000000+ 36.72058424i [14,] -1e-30+0i 1.000000+0i 1.0000000+0i 69.1934843-3.141593i -44.04994023+2.000000e+00i -1.0000000- 44.04994023i 3.0000000+ 44.04994023i [15,] -1e-35+0i 1.000000+0i 1.0000000+0i 80.7064098-3.141593i -51.37929622+2.000000e+00i -1.0000000- 51.37929622i 3.0000000+ 51.37929622i [16,] -1e-40+0i 1.000000+0i 1.0000000+0i 92.2193352-3.141593i -58.70865221+2.000000e+00i -1.0000000- 58.70865221i 3.0000000+ 58.70865221i [17,] -1e-45+0i 1.000000+0i 1.0000000+0i 103.7322607-3.141593i -66.03800819+2.000000e+00i -1.0000000- 66.03800819i 3.0000000+ 66.03800819i [18,] -1e-50+0i 1.000000+0i 1.0000000+0i 115.2451862-3.141593i -73.36736418+2.000000e+00i -1.0000000- 73.36736418i 3.0000000+ 73.36736418i [19,] -1e-60+0i 1.000000+0i 1.0000000+0i 138.2710371-3.141593i -88.02607616+2.000000e+00i -1.0000000- 88.02607616i 3.0000000+ 88.02607616i [20,] -1e-80+0i 1.000000+0i 1.0000000+0i 184.3227390-3.141593i -117.34350012+2.000000e+00i -1.0000000-117.34350012i 3.0000000+117.34350012i [21,] -1e-100+0i 1.000000+0i 1.0000000+0i 230.3744408-3.141593i -146.66092407+2.000000e+00i -1.0000000-146.66092407i 3.0000000+146.66092407i [22,] -1e-120+0i 1.000000+0i 1.0000000+0i 276.4261427-3.141593i -175.97834803+2.000000e+00i -1.0000000-175.97834803i 3.0000000+175.97834803i [23,] -1e-140+0i 1.000000+0i 1.0000000+0i 322.4778445-3.141593i -205.29577198+2.000000e+00i -1.0000000-205.29577198i 3.0000000+205.29577198i [24,] -1e-160+0i 1.000000+0i 1.0000000+0i 368.5295464-3.141593i -234.61319594+2.000000e+00i -1.0000000-234.61319594i 3.0000000+234.61319594i [25,] -1e-180+0i 1.000000+0i 1.0000000+0i 414.5812483-3.141593i -263.93061989+2.000000e+00i -1.0000000-263.93061989i 3.0000000+263.93061989i [26,] -1e-200+0i 1.000000+0i 1.0000000+0i 460.6329501-3.141593i -293.24804385+2.000000e+00i -1.0000000-293.24804385i 3.0000000+293.24804385i [27,] -1e-250+0i 1.000000+0i 1.0000000+0i 575.7622048-3.141593i -366.54160373+2.000000e+00i -1.0000000-366.54160373i 3.0000000+366.54160373i [28,] -1e-300+0i 1.000000+0i 1.0000000+0i 690.8914594-3.141593i -439.83516362+2.000000e+00i -1.0000000-439.83516362i 3.0000000+439.83516362i [29,] 1e-300+0i 1.000000+0i 1.0000000+0i 690.8914594+0.000000i -439.83516362+0.000000e+00i 1.0000000-439.83516362i 1.0000000+439.83516362i [30,] 1e-250+0i 1.000000+0i 1.0000000+0i 575.7622048+0.000000i -366.54160373+0.000000e+00i 1.0000000-366.54160373i 1.0000000+366.54160373i [31,] 1e-200+0i 1.000000+0i 1.0000000+0i 460.6329501+0.000000i -293.24804385+0.000000e+00i 1.0000000-293.24804385i 1.0000000+293.24804385i [32,] 1e-180+0i 1.000000+0i 1.0000000+0i 414.5812483+0.000000i -263.93061989+0.000000e+00i 1.0000000-263.93061989i 1.0000000+263.93061989i [33,] 1e-160+0i 1.000000+0i 1.0000000+0i 368.5295464+0.000000i -234.61319594+0.000000e+00i 1.0000000-234.61319594i 1.0000000+234.61319594i [34,] 1e-140+0i 1.000000+0i 1.0000000+0i 322.4778445+0.000000i -205.29577198+0.000000e+00i 1.0000000-205.29577198i 1.0000000+205.29577198i [35,] 1e-120+0i 1.000000+0i 1.0000000+0i 276.4261427+0.000000i -175.97834803+0.000000e+00i 1.0000000-175.97834803i 1.0000000+175.97834803i [36,] 1e-100+0i 1.000000+0i 1.0000000+0i 230.3744408+0.000000i -146.66092407+0.000000e+00i 1.0000000-146.66092407i 1.0000000+146.66092407i [37,] 1e-80+0i 1.000000+0i 1.0000000+0i 184.3227390+0.000000i -117.34350012+0.000000e+00i 1.0000000-117.34350012i 1.0000000+117.34350012i [38,] 1e-60+0i 1.000000+0i 1.0000000+0i 138.2710371+0.000000i -88.02607616+0.000000e+00i 1.0000000- 88.02607616i 1.0000000+ 88.02607616i [39,] 1e-50+0i 1.000000+0i 1.0000000+0i 115.2451862+0.000000i -73.36736418+0.000000e+00i 1.0000000- 73.36736418i 1.0000000+ 73.36736418i [40,] 1e-45+0i 1.000000+0i 1.0000000+0i 103.7322607+0.000000i -66.03800819+0.000000e+00i 1.0000000- 66.03800819i 1.0000000+ 66.03800819i [41,] 1e-40+0i 1.000000+0i 1.0000000+0i 92.2193352+0.000000i -58.70865221+0.000000e+00i 1.0000000- 58.70865221i 1.0000000+ 58.70865221i [42,] 1e-35+0i 1.000000+0i 1.0000000+0i 80.7064098+0.000000i -51.37929622+0.000000e+00i 1.0000000- 51.37929622i 1.0000000+ 51.37929622i [43,] 1e-30+0i 1.000000+0i 1.0000000+0i 69.1934843+0.000000i -44.04994023+0.000000e+00i 1.0000000- 44.04994023i 1.0000000+ 44.04994023i [44,] 1e-25+0i 1.000000+0i 1.0000000+0i 57.6805588+0.000000i -36.72058424+0.000000e+00i 1.0000000- 36.72058424i 1.0000000+ 36.72058424i [45,] 1e-20+0i 1.000000+0i 1.0000000+0i 46.1676334+0.000000i -29.39122825+0.000000e+00i 1.0000000- 29.39122825i 1.0000000+ 29.39122825i [46,] 1e-15+0i 1.000000+0i 1.0000000+0i 34.6547079+0.000000i -22.06187226+0.000000e+00i 1.0000000- 22.06187226i 1.0000000+ 22.06187226i [47,] 1e-10+0i 1.000000+0i 1.0000000+0i 23.1417824+0.000000i -14.73251627+0.000000e+00i 1.0000000- 14.73251627i 1.0000000+ 14.73251627i [48,] 1e-08+0i 1.000000+0i 1.0000000+0i 18.5366123+0.000000i -11.80077388+0.000000e+00i 1.0000000- 11.80077388i 1.0000000+ 11.80077388i [49,] 1e-07+0i 1.000000+0i 1.0000000+0i 16.2340272+0.000000i -10.33490268+0.000000e+00i 1.0000000- 10.33490268i 1.0000000+ 10.33490268i [50,] 1e-06+0i 1.000000+0i 1.0000000+0i 13.9314421+0.000000i -8.86903148+0.000000e+00i 1.0000000- 8.86903148i 1.0000000+ 8.86903148i [51,] 1e-05+0i 1.000000+0i 1.0000000+0i 11.6288570+0.000000i -7.40316028+0.000000e+00i 1.0000000- 7.40316028i 1.0000000+ 7.40316028i [52,] 1e-04+0i 1.000000+0i 1.0000000+0i 9.3262719+0.000000i -5.93728907-1.110223e-16i 1.0000000- 5.93728907i 1.0000000+ 5.93728907i [53,] 1e-03+0i 1.000000+0i 0.9999998+0i 7.0236888+0.000000i -4.47141661-1.110223e-16i 0.9999998- 4.47141661i 0.9999998+ 4.47141661i [54,] 1e-02+0i 1.000025+0i 0.9999750+0i 4.7212447+0.000000i -3.00545564-1.110223e-16i 0.9999750- 3.00545564i 0.9999750+ 3.00545564i [55,] 1e-01+0i 1.002502+0i 0.9975016+0i 2.4270690+0.000000i -1.53423865+0.000000e+00i 0.9975016- 1.53423865i 0.9975016+ 1.53423865i [56,] 1e+00+0i 1.266066+0i 0.7651977+0i 0.4210244+0.000000i 0.08825696+2.220446e-16i 0.7651977+ 0.08825696i 0.7651977- 0.08825696i > (BRs1 <- allBessel(xs., 1)) x I J K Y H1 [1,] -1e+00+0i -5.651591e-01+0i -4.400506e-01+0i -6.019072e-01- 1.775500e+00i 7.812128e-01- 8.801012e-01i 4.400506e-01+ 7.812128e-01i [2,] -1e-01+0i -5.006253e-02+0i -4.993753e-02+0i -9.853845e+00- 1.572761e-01i 6.458951e+00- 9.987505e-02i 4.993753e-02+ 6.458951e+00i [3,] -1e-02+0i -5.000063e-03+0i -4.999938e-03+0i -9.997389e+01- 1.570816e-02i 6.367860e+01- 9.999875e-03i 4.999938e-03+ 6.367860e+01i [4,] -1e-03+0i -5.000001e-04+0i -4.999999e-04+0i -9.999962e+02- 1.570797e-03i 6.366222e+02- 9.999999e-04i 4.999999e-04+ 6.366222e+02i [5,] -1e-04+0i -5.000000e-05+0i -5.000000e-05+0i -1.000000e+04- 1.570796e-04i 6.366198e+03- 1.000000e-04i 5.000000e-05+ 6.366198e+03i [6,] -1e-05+0i -5.000000e-06+0i -5.000000e-06+0i -1.000000e+05- 1.570796e-05i 6.366198e+04- 1.000000e-05i 4.999996e-06+ 6.366198e+04i [7,] -1e-06+0i -5.000000e-07+0i -5.000000e-07+0i -1.000000e+06- 1.570796e-06i 6.366198e+05- 1.000000e-06i 4.999610e-07+ 6.366198e+05i [8,] -1e-07+0i -5.000000e-08+0i -5.000000e-08+0i -1.000000e+07- 1.570796e-07i 6.366198e+06- 1.000000e-07i 4.961020e-08+ 6.366198e+06i [9,] -1e-08+0i -5.000000e-09+0i -5.000000e-09+0i -1.000000e+08- 1.570796e-08i 6.366198e+07- 1.000000e-08i 1.101957e-09+ 6.366198e+07i [10,] -1e-10+0i -5.000000e-11+0i -5.000000e-11+0i -1.000000e+10- 1.570796e-10i 6.366198e+09- 1.000000e-10i -3.897543e-07+ 6.366198e+09i [11,] -1e-15+0i -5.000000e-16+0i -5.000000e-16+0i -1.000000e+15- 1.570796e-15i 6.366198e+14- 1.000000e-15i -3.898043e-02+ 6.366198e+14i [12,] -1e-20+0i -5.000000e-21+0i -5.000000e-21+0i -1.000000e+20- 1.570796e-20i 6.366198e+19- 5.000000e-21i -3.898043e+03+ 6.366198e+19i [13,] -1e-25+0i -5.000000e-26+0i -5.000000e-26+0i -1.000000e+25- 1.570796e-25i 6.366198e+24- 5.000000e-26i -3.898043e+08+ 6.366198e+24i [14,] -1e-30+0i -5.000000e-31+0i -5.000000e-31+0i -1.000000e+30- 1.570796e-30i 6.366198e+29- 5.000000e-31i -3.898043e+13+ 6.366198e+29i [15,] -1e-35+0i -5.000000e-36+0i -5.000000e-36+0i -1.000000e+35- 1.570796e-35i 6.366198e+34- 5.000000e-36i -3.898043e+18+ 6.366198e+34i [16,] -1e-40+0i -5.000000e-41+0i -5.000000e-41+0i -1.000000e+40- 1.570796e-40i 6.366198e+39- 5.000000e-41i -3.898043e+23+ 6.366198e+39i [17,] -1e-45+0i -5.000000e-46+0i -5.000000e-46+0i -1.000000e+45- 1.570796e-45i 6.366198e+44- 5.000000e-46i -3.898043e+28+ 6.366198e+44i [18,] -1e-50+0i -5.000000e-51+0i -5.000000e-51+0i -1.000000e+50- 1.570796e-50i 6.366198e+49- 5.000000e-51i -3.898043e+33+ 6.366198e+49i [19,] -1e-60+0i -5.000000e-61+0i -5.000000e-61+0i -1.000000e+60- 1.570796e-60i 6.366198e+59- 5.000000e-61i -3.898043e+43+ 6.366198e+59i [20,] -1e-80+0i -5.000000e-81+0i -5.000000e-81+0i -1.000000e+80- 1.570796e-80i 6.366198e+79- 5.000000e-81i -3.898043e+63+ 6.366198e+79i [21,] -1e-100+0i -5.000000e-101+0i -5.000000e-101+0i -1.000000e+100-1.570796e-100i 6.366198e+99-5.000000e-101i -3.898043e+83+ 6.366198e+99i [22,] -1e-120+0i -5.000000e-121+0i -5.000000e-121+0i -1.000000e+120-1.570796e-120i 6.366198e+119-5.000000e-121i -3.898043e+103+6.366198e+119i [23,] -1e-140+0i -5.000000e-141+0i -5.000000e-141+0i -1.000000e+140-1.570796e-140i 6.366198e+139-5.000000e-141i -3.898043e+123+6.366198e+139i [24,] -1e-160+0i -5.000000e-161+0i -5.000000e-161+0i -1.000000e+160-1.570796e-160i 6.366198e+159-5.000000e-161i -3.898043e+143+6.366198e+159i [25,] -1e-180+0i -5.000000e-181+0i -5.000000e-181+0i -1.000000e+180-1.570796e-180i 6.366198e+179-5.000000e-181i -3.898043e+163+6.366198e+179i [26,] -1e-200+0i -5.000000e-201+0i -5.000000e-201+0i -1.000000e+200-1.570796e-200i 6.366198e+199-5.000000e-201i -3.898043e+183+6.366198e+199i [27,] -1e-250+0i -5.000000e-251+0i -5.000000e-251+0i -1.000000e+250-1.570796e-250i 6.366198e+249-5.000000e-251i -3.898043e+233+6.366198e+249i [28,] -1e-300+0i -5.000000e-301+0i -5.000000e-301+0i -1.000000e+300-1.570796e-300i 6.366198e+299-5.000000e-301i -3.898043e+283+6.366198e+299i [29,] 1e-300+0i 5.000000e-301+0i 5.000000e-301+0i 1.000000e+300+ 0.000000e+00i -6.366198e+299+5.000000e-301i 3.898043e+283-6.366198e+299i [30,] 1e-250+0i 5.000000e-251+0i 5.000000e-251+0i 1.000000e+250+ 0.000000e+00i -6.366198e+249+5.000000e-251i 3.898043e+233-6.366198e+249i [31,] 1e-200+0i 5.000000e-201+0i 5.000000e-201+0i 1.000000e+200+ 0.000000e+00i -6.366198e+199+5.000000e-201i 3.898043e+183-6.366198e+199i [32,] 1e-180+0i 5.000000e-181+0i 5.000000e-181+0i 1.000000e+180+ 0.000000e+00i -6.366198e+179+5.000000e-181i 3.898043e+163-6.366198e+179i [33,] 1e-160+0i 5.000000e-161+0i 5.000000e-161+0i 1.000000e+160+ 0.000000e+00i -6.366198e+159+5.000000e-161i 3.898043e+143-6.366198e+159i [34,] 1e-140+0i 5.000000e-141+0i 5.000000e-141+0i 1.000000e+140+ 0.000000e+00i -6.366198e+139+5.000000e-141i 3.898043e+123-6.366198e+139i [35,] 1e-120+0i 5.000000e-121+0i 5.000000e-121+0i 1.000000e+120+ 0.000000e+00i -6.366198e+119+5.000000e-121i 3.898043e+103-6.366198e+119i [36,] 1e-100+0i 5.000000e-101+0i 5.000000e-101+0i 1.000000e+100+ 0.000000e+00i -6.366198e+99+5.000000e-101i 3.898043e+83- 6.366198e+99i [37,] 1e-80+0i 5.000000e-81+0i 5.000000e-81+0i 1.000000e+80+ 0.000000e+00i -6.366198e+79+ 5.000000e-81i 3.898043e+63- 6.366198e+79i [38,] 1e-60+0i 5.000000e-61+0i 5.000000e-61+0i 1.000000e+60+ 0.000000e+00i -6.366198e+59+ 5.000000e-61i 3.898043e+43- 6.366198e+59i [39,] 1e-50+0i 5.000000e-51+0i 5.000000e-51+0i 1.000000e+50+ 0.000000e+00i -6.366198e+49+ 5.000000e-51i 3.898043e+33- 6.366198e+49i [40,] 1e-45+0i 5.000000e-46+0i 5.000000e-46+0i 1.000000e+45+ 0.000000e+00i -6.366198e+44+ 5.000000e-46i 3.898043e+28- 6.366198e+44i [41,] 1e-40+0i 5.000000e-41+0i 5.000000e-41+0i 1.000000e+40+ 0.000000e+00i -6.366198e+39+ 5.000000e-41i 3.898043e+23- 6.366198e+39i [42,] 1e-35+0i 5.000000e-36+0i 5.000000e-36+0i 1.000000e+35+ 0.000000e+00i -6.366198e+34+ 5.000000e-36i 3.898043e+18- 6.366198e+34i [43,] 1e-30+0i 5.000000e-31+0i 5.000000e-31+0i 1.000000e+30+ 0.000000e+00i -6.366198e+29+ 5.000000e-31i 3.898043e+13- 6.366198e+29i [44,] 1e-25+0i 5.000000e-26+0i 5.000000e-26+0i 1.000000e+25+ 0.000000e+00i -6.366198e+24+ 5.000000e-26i 3.898043e+08- 6.366198e+24i [45,] 1e-20+0i 5.000000e-21+0i 5.000000e-21+0i 1.000000e+20+ 0.000000e+00i -6.366198e+19+ 5.000000e-21i 3.898043e+03- 6.366198e+19i [46,] 1e-15+0i 5.000000e-16+0i 5.000000e-16+0i 1.000000e+15+ 0.000000e+00i -6.366198e+14- 2.958228e-31i 3.898043e-02- 6.366198e+14i [47,] 1e-10+0i 5.000000e-11+0i 5.000000e-11+0i 1.000000e+10+ 0.000000e+00i -6.366198e+09+ 5.816114e-26i 3.898543e-07- 6.366198e+09i [48,] 1e-08+0i 5.000000e-09+0i 5.000000e-09+0i 1.000000e+08+ 0.000000e+00i -6.366198e+07+ 0.000000e+00i 8.898043e-09- 6.366198e+07i [49,] 1e-07+0i 5.000000e-08+0i 5.000000e-08+0i 1.000000e+07+ 0.000000e+00i -6.366198e+06+ 5.293956e-23i 5.038980e-08- 6.366198e+06i [50,] 1e-06+0i 5.000000e-07+0i 5.000000e-07+0i 1.000000e+06+ 0.000000e+00i -6.366198e+05+ 2.117582e-22i 5.000390e-07- 6.366198e+05i [51,] 1e-05+0i 5.000000e-06+0i 5.000000e-06+0i 1.000000e+05+ 0.000000e+00i -6.366198e+04+ 0.000000e+00i 5.000004e-06- 6.366198e+04i [52,] 1e-04+0i 5.000000e-05+0i 5.000000e-05+0i 1.000000e+04+ 0.000000e+00i -6.366198e+03+ 4.743385e-20i 5.000000e-05- 6.366198e+03i [53,] 1e-03+0i 5.000001e-04+0i 4.999999e-04+0i 9.999962e+02+ 0.000000e+00i -6.366222e+02+ 1.084202e-19i 4.999999e-04- 6.366222e+02i [54,] 1e-02+0i 5.000063e-03+0i 4.999938e-03+0i 9.997389e+01+ 0.000000e+00i -6.367860e+01+ 3.469447e-18i 4.999938e-03- 6.367860e+01i [55,] 1e-01+0i 5.006253e-02+0i 4.993753e-02+0i 9.853845e+00+ 0.000000e+00i -6.458951e+00+ 1.387779e-17i 4.993753e-02- 6.458951e+00i [56,] 1e+00+0i 5.651591e-01+0i 4.400506e-01+0i 6.019072e-01+ 0.000000e+00i -7.812128e-01+ 5.551115e-17i 4.400506e-01- 7.812128e-01i H2 [1,] -1.320152e+00- 7.812128e-01i [2,] -1.498126e-01- 6.458951e+00i [3,] -1.499981e-02- 6.367860e+01i [4,] -1.500000e-03- 6.366222e+02i [5,] -1.500000e-04- 6.366198e+03i [6,] -1.500000e-05- 6.366198e+04i [7,] -1.500039e-06- 6.366198e+05i [8,] -1.503898e-07- 6.366198e+06i [9,] -1.889804e-08- 6.366198e+07i [10,] -3.899543e-07- 6.366198e+09i [11,] -3.898043e-02- 6.366198e+14i [12,] -3.898043e+03- 6.366198e+19i [13,] -3.898043e+08- 6.366198e+24i [14,] -3.898043e+13- 6.366198e+29i [15,] -3.898043e+18- 6.366198e+34i [16,] -3.898043e+23- 6.366198e+39i [17,] -3.898043e+28- 6.366198e+44i [18,] -3.898043e+33- 6.366198e+49i [19,] -3.898043e+43- 6.366198e+59i [20,] -3.898043e+63- 6.366198e+79i [21,] -3.898043e+83- 6.366198e+99i [22,] -3.898043e+103-6.366198e+119i [23,] -3.898043e+123-6.366198e+139i [24,] -3.898043e+143-6.366198e+159i [25,] -3.898043e+163-6.366198e+179i [26,] -3.898043e+183-6.366198e+199i [27,] -3.898043e+233-6.366198e+249i [28,] -3.898043e+283-6.366198e+299i [29,] 3.898043e+283+6.366198e+299i [30,] 3.898043e+233+6.366198e+249i [31,] 3.898043e+183+6.366198e+199i [32,] 3.898043e+163+6.366198e+179i [33,] 3.898043e+143+6.366198e+159i [34,] 3.898043e+123+6.366198e+139i [35,] 3.898043e+103+6.366198e+119i [36,] 3.898043e+83+ 6.366198e+99i [37,] 3.898043e+63+ 6.366198e+79i [38,] 3.898043e+43+ 6.366198e+59i [39,] 3.898043e+33+ 6.366198e+49i [40,] 3.898043e+28+ 6.366198e+44i [41,] 3.898043e+23+ 6.366198e+39i [42,] 3.898043e+18+ 6.366198e+34i [43,] 3.898043e+13+ 6.366198e+29i [44,] 3.898043e+08+ 6.366198e+24i [45,] 3.898043e+03+ 6.366198e+19i [46,] 3.898043e-02+ 6.366198e+14i [47,] 3.898543e-07+ 6.366198e+09i [48,] 8.898043e-09+ 6.366198e+07i [49,] 5.038980e-08+ 6.366198e+06i [50,] 5.000390e-07+ 6.366198e+05i [51,] 5.000004e-06+ 6.366198e+04i [52,] 5.000000e-05+ 6.366198e+03i [53,] 4.999999e-04+ 6.366222e+02i [54,] 4.999938e-03+ 6.367860e+01i [55,] 4.993753e-02+ 6.458951e+00i [56,] 4.400506e-01+ 7.812128e-01i > > (BRs3 <- allBessel(xs., 3)) x I J K Y H1 [1,] -1e+00+0i -2.216842e-02+0i -1.956335e-02+0i -7.101263e+00- 6.964416e-02i 5.821518e+00- 3.912671e-02i 1.956335e-02+ 5.821518e+00i [2,] -1e-01+0i -2.084636e-05+0i -2.082032e-05+0i -7.990012e+03- 6.549076e-05i 5.099332e+03- 4.164063e-05i 2.082032e-05+ 5.099332e+03i [3,] -1e-02+0i -2.083346e-08+0i -2.083320e-08+0i -7.999900e+06- 6.545026e-08i 5.093022e+06- 4.166636e-08i 2.052131e-08+ 5.093022e+06i [4,] -1e-03+0i -2.083333e-11+0i -2.083333e-11+0i -7.999999e+09- 6.544985e-11i 5.092959e+09- 4.148936e-11i -3.118228e-07+ 5.092959e+09i [5,] -1e-04+0i -2.083333e-14+0i -2.083333e-14+0i -8.000000e+12- 6.544985e-14i 5.092958e+12+ 6.645508e-12i -3.118435e-04+ 5.092958e+12i [6,] -1e-05+0i -2.083333e-17+0i -2.083333e-17+0i -8.000000e+15- 6.544985e-17i 5.092958e+15+ 2.245839e-10i -3.118434e-01+ 5.092958e+15i [7,] -1e-06+0i -2.083333e-20+0i -2.083333e-20+0i -8.000000e+18- 6.544985e-20i 5.092958e+18+ 1.581621e-10i -3.118434e+02+ 5.092958e+18i [8,] -1e-07+0i -2.083333e-23+0i -2.083333e-23+0i -8.000000e+21- 6.544985e-23i 5.092958e+21- 8.888749e-10i -3.118434e+05+ 5.092958e+21i [9,] -1e-08+0i -2.083333e-26+0i -2.083333e-26+0i -8.000000e+24- 6.544985e-26i 5.092958e+24+ 5.000000e-09i -3.118434e+08+ 5.092958e+24i [10,] -1e-10+0i -2.083333e-32+0i -2.083333e-32+0i -8.000000e+30- 6.544985e-32i 5.092958e+30- 5.654269e-06i -3.118434e+14+ 5.092958e+30i [11,] -1e-15+0i -2.083333e-47+0i -2.083333e-47+0i -8.000000e+45- 6.544985e-47i 5.092958e+45+ 5.654319e-01i -3.118434e+29+ 5.092958e+45i [12,] -1e-20+0i -2.083333e-62+0i -2.083333e-62+0i -8.000000e+60- 6.544985e-62i 5.092958e+60+ 4.000000e+20i -3.118434e+44+ 5.092958e+60i [13,] -1e-25+0i -2.083333e-77+0i -2.083333e-77+0i -8.000000e+75- 6.544985e-77i 5.092958e+75+ 4.000000e+25i -3.118434e+59+ 5.092958e+75i [14,] -1e-30+0i -2.083333e-92+0i -2.083333e-92+0i -8.000000e+90- 6.544985e-92i 5.092958e+90+ 4.000000e+30i -3.118434e+74+ 5.092958e+90i [15,] -1e-35+0i -2.083333e-107+0i -2.083333e-107+0i -8.000000e+105-6.544985e-107i 5.092958e+105+ 4.000000e+35i -3.118434e+89+5.092958e+105i [16,] -1e-40+0i -2.083333e-122+0i -2.083333e-122+0i -8.000000e+120-6.544985e-122i 5.092958e+120+ 4.000000e+40i -3.118434e+104+5.092958e+120i [17,] -1e-45+0i -2.083333e-137+0i -2.083333e-137+0i -8.000000e+135-6.544985e-137i 5.092958e+135+ 4.000000e+45i -3.118434e+119+5.092958e+135i [18,] -1e-50+0i -2.083333e-152+0i -2.083333e-152+0i -8.000000e+150-6.544985e-152i 5.092958e+150+ 4.000000e+50i -3.118434e+134+5.092958e+150i [19,] -1e-60+0i -2.083333e-182+0i -2.083333e-182+0i -8.000000e+180-6.544985e-182i 5.092958e+180+ 4.000000e+60i -3.118434e+164+5.092958e+180i [20,] -1e-80+0i -2.083333e-242+0i -2.083333e-242+0i -8.000000e+240-6.544985e-242i 5.092958e+240+ 4.000000e+80i -3.118434e+224+5.092958e+240i [21,] -1e-100+0i -2.083333e-302+0i -2.083333e-302+0i -8.000000e+300-6.544985e-302i 5.092958e+300+4.000000e+100i -3.118434e+284+5.092958e+300i [22,] -1e-120+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [23,] -1e-140+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [24,] -1e-160+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [25,] -1e-180+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [26,] -1e-200+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [27,] -1e-250+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [28,] -1e-300+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [29,] 1e-300+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [30,] 1e-250+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [31,] 1e-200+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [32,] 1e-180+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [33,] 1e-160+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [34,] 1e-140+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [35,] 1e-120+0i 0.000000e+00+0i 0.000000e+00+0i Inf+ Infi Inf+ Infi Inf+ Infi [36,] 1e-100+0i 2.083333e-302+0i 2.083333e-302+0i 8.000000e+300+ 0.000000e+00i -5.092958e+300+4.000000e+100i 3.118434e+284-5.092958e+300i [37,] 1e-80+0i 2.083333e-242+0i 2.083333e-242+0i 8.000000e+240+ 0.000000e+00i -5.092958e+240+ 4.000000e+80i 3.118434e+224-5.092958e+240i [38,] 1e-60+0i 2.083333e-182+0i 2.083333e-182+0i 8.000000e+180+ 0.000000e+00i -5.092958e+180+ 4.000000e+60i 3.118434e+164-5.092958e+180i [39,] 1e-50+0i 2.083333e-152+0i 2.083333e-152+0i 8.000000e+150+ 0.000000e+00i -5.092958e+150+ 4.000000e+50i 3.118434e+134-5.092958e+150i [40,] 1e-45+0i 2.083333e-137+0i 2.083333e-137+0i 8.000000e+135+ 0.000000e+00i -5.092958e+135+ 4.000000e+45i 3.118434e+119-5.092958e+135i [41,] 1e-40+0i 2.083333e-122+0i 2.083333e-122+0i 8.000000e+120+ 0.000000e+00i -5.092958e+120+ 4.000000e+40i 3.118434e+104-5.092958e+120i [42,] 1e-35+0i 2.083333e-107+0i 2.083333e-107+0i 8.000000e+105+ 0.000000e+00i -5.092958e+105+ 4.000000e+35i 3.118434e+89-5.092958e+105i [43,] 1e-30+0i 2.083333e-92+0i 2.083333e-92+0i 8.000000e+90+ 0.000000e+00i -5.092958e+90+ 4.000000e+30i 3.118434e+74- 5.092958e+90i [44,] 1e-25+0i 2.083333e-77+0i 2.083333e-77+0i 8.000000e+75+ 0.000000e+00i -5.092958e+75+ 4.000000e+25i 3.118434e+59- 5.092958e+75i [45,] 1e-20+0i 2.083333e-62+0i 2.083333e-62+0i 8.000000e+60+ 0.000000e+00i -5.092958e+60+ 4.000000e+20i 3.118434e+44- 5.092958e+60i [46,] 1e-15+0i 2.083333e-47+0i 2.083333e-47+0i 8.000000e+45+ 0.000000e+00i -5.092958e+45+ 5.654319e-01i 3.118434e+29- 5.092958e+45i [47,] 1e-10+0i 2.083333e-32+0i 2.083333e-32+0i 8.000000e+30+ 0.000000e+00i -5.092958e+30- 5.654269e-06i 3.118434e+14- 5.092958e+30i [48,] 1e-08+0i 2.083333e-26+0i 2.083333e-26+0i 8.000000e+24+ 0.000000e+00i -5.092958e+24+ 5.000000e-09i 3.118434e+08- 5.092958e+24i [49,] 1e-07+0i 2.083333e-23+0i 2.083333e-23+0i 8.000000e+21+ 0.000000e+00i -5.092958e+21- 8.888749e-10i 3.118434e+05- 5.092958e+21i [50,] 1e-06+0i 2.083333e-20+0i 2.083333e-20+0i 8.000000e+18+ 0.000000e+00i -5.092958e+18+ 1.581621e-10i 3.118434e+02- 5.092958e+18i [51,] 1e-05+0i 2.083333e-17+0i 2.083333e-17+0i 8.000000e+15+ 0.000000e+00i -5.092958e+15+ 2.245839e-10i 3.118434e-01- 5.092958e+15i [52,] 1e-04+0i 2.083333e-14+0i 2.083333e-14+0i 8.000000e+12+ 0.000000e+00i -5.092958e+12+ 6.687174e-12i 3.118434e-04- 5.092958e+12i [53,] 1e-03+0i 2.083333e-11+0i 2.083333e-11+0i 7.999999e+09+ 0.000000e+00i -5.092959e+09+ 1.773086e-13i 3.118641e-07- 5.092959e+09i [54,] 1e-02+0i 2.083346e-08+0i 2.083320e-08+0i 7.999900e+06+ 0.000000e+00i -5.093022e+06+ 5.046231e-14i 2.114500e-08- 5.093022e+06i [55,] 1e-01+0i 2.084636e-05+0i 2.082032e-05+0i 7.990012e+03+ 0.000000e+00i -5.099332e+03+ 6.742680e-15i 2.082032e-05- 5.099332e+03i [56,] 1e+00+0i 2.216842e-02+0i 1.956335e-02+0i 7.101263e+00+ 0.000000e+00i -5.821518e+00- 3.781697e-16i 1.956335e-02- 5.821518e+00i H2 [1,] -5.869006e-02- 5.821518e+00i [2,] -6.246095e-05- 5.099332e+03i [3,] -6.281141e-08- 5.093022e+06i [4,] -3.119058e-07- 5.092959e+09i [5,] -3.118434e-04- 5.092958e+12i [6,] -3.118434e-01- 5.092958e+15i [7,] -3.118434e+02- 5.092958e+18i [8,] -3.118434e+05- 5.092958e+21i [9,] -3.118434e+08- 5.092958e+24i [10,] -3.118434e+14- 5.092958e+30i [11,] -3.118434e+29- 5.092958e+45i [12,] -3.118434e+44- 5.092958e+60i [13,] -3.118434e+59- 5.092958e+75i [14,] -3.118434e+74- 5.092958e+90i [15,] -3.118434e+89-5.092958e+105i [16,] -3.118434e+104-5.092958e+120i [17,] -3.118434e+119-5.092958e+135i [18,] -3.118434e+134-5.092958e+150i [19,] -3.118434e+164-5.092958e+180i [20,] -3.118434e+224-5.092958e+240i [21,] -3.118434e+284-5.092958e+300i [22,] Inf+ Infi [23,] Inf+ Infi [24,] Inf+ Infi [25,] Inf+ Infi [26,] Inf+ Infi [27,] Inf+ Infi [28,] Inf+ Infi [29,] Inf+ Infi [30,] Inf+ Infi [31,] Inf+ Infi [32,] Inf+ Infi [33,] Inf+ Infi [34,] Inf+ Infi [35,] Inf+ Infi [36,] 3.118434e+284+5.092958e+300i [37,] 3.118434e+224+5.092958e+240i [38,] 3.118434e+164+5.092958e+180i [39,] 3.118434e+134+5.092958e+150i [40,] 3.118434e+119+5.092958e+135i [41,] 3.118434e+104+5.092958e+120i [42,] 3.118434e+89+5.092958e+105i [43,] 3.118434e+74+ 5.092958e+90i [44,] 3.118434e+59+ 5.092958e+75i [45,] 3.118434e+44+ 5.092958e+60i [46,] 3.118434e+29+ 5.092958e+45i [47,] 3.118434e+14+ 5.092958e+30i [48,] 3.118434e+08+ 5.092958e+24i [49,] 3.118434e+05+ 5.092958e+21i [50,] 3.118434e+02+ 5.092958e+18i [51,] 3.118434e-01+ 5.092958e+15i [52,] 3.118434e-04+ 5.092958e+12i [53,] 3.118641e-07+ 5.092959e+09i [54,] 2.114500e-08+ 5.093022e+06i [55,] 2.082032e-05+ 5.099332e+03i [56,] 1.956335e-02+ 5.821518e+00i > > > > > options(op) > cat('Time elapsed: ', proc.time(),'\n') # for ''statistical reasons'' Time elapsed: 2.21 0.31 2.51 NA NA > > proc.time() user system elapsed 2.21 0.31 2.51