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Type 'q()' to quit R. > ####=== Numerical / Arithmetic Tests > ####--- ALL tests here should return TRUE ! > ### > ### '##P': These lines don't give TRUE but relevant ``Print output'' > > ### --> d-p-q-r-tests.R & d-p-q-r-tst-2.R for distribution things > > .proctime00 <- proc.time() > opt.conformance <- 0 > Meps <- .Machine $ double.eps > > ## this uses random inputs, so set the seed > set.seed(1) > > options(rErr.eps = 1e-30) > rErr <- function(approx, true, eps = .Options$rErr.eps) + { + if(is.null(eps)) { eps <- 1e-30; options(rErr.eps = eps) } + ifelse(Mod(true) >= eps, + 1 - approx / true, # relative error + true - approx) # absolute error (e.g. when true=0) + } > > abs(1- .Machine$double.xmin * 10^(-.Machine$double.min.exp*log10(2)))/Meps < 1e3 [1] TRUE > ##P (1- .Machine$double.xmin * 10^(-.Machine$double.min.exp*log10(2)))/Meps > if(opt.conformance)#fails at least on SGI/IRIX 6.5 + abs(1- .Machine$double.xmax * 10^(-.Machine$double.max.exp*log10(2)))/Meps < 1e3 > > ## More IEEE Infinity/NaN checks > i1 <- pi / 0 > i1 == (i2 <- 1:1 / 0:0) [1] TRUE > is.infinite( i1) & is.infinite( i2) & i1 > 12 & i2 > 12 [1] TRUE > is.infinite(-i1) & is.infinite(-i2) & (-i1) < -12 & (-i2) < -12 [1] TRUE > > is.nan(n1 <- 0 / 0) [1] TRUE > is.nan( - n1) [1] TRUE > > i1 == i1 + i1 [1] TRUE > i1 == i1 * i1 [1] TRUE > is.nan(i1 - i1) [1] TRUE > is.nan(i1 / i1) [1] TRUE > > 1/0 == Inf & 0 ^ -1 == Inf [1] TRUE > 1/Inf == 0 & Inf ^ -1 == 0 [1] TRUE > > iNA <- as.integer(NA) > !is.na(Inf) & !is.nan(Inf) & is.infinite(Inf) & !is.finite(Inf) [1] TRUE > !is.na(-Inf)& !is.nan(-Inf)& is.infinite(-Inf)& !is.finite(-Inf) [1] TRUE > is.na(NA) & !is.nan(NA) & !is.infinite(NA) & !is.finite(NA) [1] TRUE > is.na(NaN) & is.nan(NaN) & !is.infinite(NaN) & !is.finite(NaN) [1] TRUE > is.na(iNA) & !is.nan(iNA) & !is.infinite(iNA) & !is.finite(iNA) [1] TRUE > > ## These are "double"s: > all(!is.nan(c(1.,NA))) [1] TRUE > all(c(FALSE,TRUE,FALSE) == is.nan(c (1.,NaN,NA))) [1] TRUE > ## lists are no longer allowed > ## all(c(FALSE,TRUE,FALSE) == is.nan(list(1.,NaN,NA))) > > > ## log() and "pow()" -- POSIX is not specific enough.. > log(0) == -Inf [1] TRUE > is.nan(log(-1))# TRUE and warning [1] TRUE Warning message: In log(-1) : NaNs produced > > rp <- c(1:2,Inf); rn <- rev(- rp) > r <- c(rn, 0, rp, NA, NaN) > all(r^0 == 1) [1] TRUE > ir <- suppressWarnings(as.integer(r)) > all(ir^0 == 1) [1] TRUE > all(ir^0L == 1)# not in R <= 2.15.0 [1] TRUE > all( 1^r == 1)# not in R 0.64 [1] TRUE > all(1L^r == 1) [1] TRUE > all(1L^ir == 1)# not in R <= 2.15.0 [1] TRUE > all((rn ^ -3) == -((-rn) ^ -3)) [1] TRUE > # > all(c(1.1,2,Inf) ^ Inf == Inf) [1] TRUE > all(c(1.1,2,Inf) ^ -Inf == 0) [1] TRUE > .9 ^ Inf == 0 [1] TRUE > .9 ^ -Inf == Inf [1] TRUE > ## Wasn't ok in 0.64: > all(is.nan(rn ^ .5))# in some C's : (-Inf) ^ .5 gives Inf, instead of NaN [1] TRUE > > > ## Real Trig.: > cos(0) == 1 [1] TRUE > sin(3*pi/2) == cos(pi) [1] TRUE > x <- rnorm(99) > all( sin(-x) == - sin(x)) [1] TRUE > all( cos(-x) == cos(x)) [1] TRUE > > x <- 1:99/100 > all(abs(1 - x / asin(sin(x))) <= 2*Meps)# "== 2*" for HP-UX [1] TRUE > all(abs(1 - x / atan(tan(x))) < 2*Meps) [1] TRUE > > ## Sun has asin(.) = acos(.) = 0 for these: > ## is.nan(acos(1.1)) && is.nan(asin(-2)) [!] > > ## gamma() > abs(gamma(1/2)^2 - pi) < 4* Meps [1] TRUE > r <- rlnorm(5000) # NB random, and next has failed for some seed > all(abs(rErr(gamma(r+1), r*gamma(r))) < 500 * Meps) [1] TRUE > ## more accurate for integers n <= 50 since R 1.8.0 Sol8: perfect > n <- 20; all( gamma(1:n) == cumprod(c(1,1:(n-1))))# Lnx: up too n=28 [1] TRUE > n <- 50; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 20*Meps)#Lnx: f=2 [1] TRUE > n <- 120; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 1000*Meps) [1] TRUE > n <- 10000;all(abs(rErr(lgamma(1:n),cumsum(log(c(1,1:(n-1)))))) < 100*Meps) [1] TRUE > > n <- 10; all( gamma(1:n) == cumprod(c(1,1:(n-1)))) [1] TRUE > n <- 20; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 100*Meps) [1] TRUE > n <- 120; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 1000*Meps) [1] TRUE > n <- 10000;all(abs(rErr(lgamma(1:n),cumsum(log(c(1,1:(n-1)))))) < 100*Meps) [1] TRUE > > all(is.nan(gamma(0:-47))) # + warn. [1] TRUE Warning message: In gamma(0:-47) : NaNs produced > > ## choose() {and lchoose}: > n51 <- c(196793068630200, 229591913401900, 247959266474052) > abs(c(n51, rev(n51))- choose(51, 23:28)) <= 2 [1] TRUE TRUE TRUE TRUE TRUE TRUE > all(choose(0:4,2) == c(0,0,1,3,6)) [1] TRUE > ## 3 to 8 units off and two NaN's in 1.8.1 > > ## psi[gamma](x) and derivatives: > ## psi == digamma: > gEuler <- 0.577215664901532860606512# = Euler's gamma > abs(digamma(1) + gEuler) < 32*Meps # i386 Lx: = 2.5*Meps [1] TRUE > all.equal(digamma(1) - digamma(1/2), log(4), tolerance = 32*Meps)# Linux: < 1*Meps! [1] TRUE > n <- 1:12 > all.equal(digamma(n), + - gEuler + c(0, cumsum(1/n)[-length(n)]),tolerance = 32*Meps)#i386 Lx: 1.3 Meps [1] TRUE > all.equal(digamma(n + 1/2), + - gEuler - log(4) + 2*cumsum(1/(2*n-1)),tolerance = 32*Meps)#i386 Lx: 1.8 Meps [1] TRUE > ## higher psigamma: > all.equal(psigamma(1, deriv=c(1,3,5)), + pi^(2*(1:3)) * c(1/6, 1/15, 8/63), tolerance = 32*Meps) [1] TRUE > x <- c(-100,-3:2, -99.9, -7.7, seq(-3,3, length=61), 5.1, 77) > ## Intel icc showed a < 1ulp difference in the second. > stopifnot(all.equal( digamma(x), psigamma(x,0), tolerance = 2*Meps), + all.equal(trigamma(x), psigamma(x,1), tolerance = 2*Meps))# TRUE (+ NaN warnings) Warning messages: 1: In digamma(x) : NaNs produced 2: In psigamma(x, 0) : NaNs produced > ## very large x: > x <- 1e30 ^ (1:10) > a.relE <- function(appr, true) abs(1 - appr/true) > stopifnot(a.relE(digamma(x), log(x)) < 1e-13, + a.relE(trigamma(x), 1/x) < 1e-13) > x <- sqrt(x[2:6]); stopifnot(a.relE(psigamma(x,2), - 1/x^2) < 1e-13) > x <- 10^(10*(2:6));stopifnot(a.relE(psigamma(x,5), +24/x^5) < 1e-13) > > ## fft(): > ok <- TRUE > ##test EXTENSIVELY: for(N in 1:100) { > cat(".") .> for(n in c(1:30, 1000:1050)) { + x <- rnorm(n) + er <- Mod(rErr(fft(fft(x), inverse = TRUE)/n, x*(1+0i))) + n.ok <- all(er < 1e-8) & quantile(er, 0.95, names=FALSE) < 10000*Meps + if(!n.ok) cat("\nn=",n,": quantile(rErr, c(.95,1)) =", + formatC(quantile(er, prob= c(.95,1))),"\n") + ok <- ok & n.ok + } > cat("\n") > ##test EXTENSIVELY: } > ok [1] TRUE > > ## var(): > for(n in 2:10) + print(all.equal(n*(n-1)*var(diag(n)), + matrix(c(rep(c(n-1,rep(-1,n)),n-1), n-1), nr=n, nc=n), + tolerance = 20*Meps)) # use tolerance = 0 to see rel.error [1] TRUE [1] TRUE [1] TRUE [1] TRUE [1] TRUE [1] TRUE [1] TRUE [1] TRUE [1] TRUE > > ## pmin() & pmax() -- "attributes" ! > v1 <- c(a=2) > m1 <- cbind( 2:4,3) > m2 <- cbind(a=2:4,2) > > all( pmax(v1, 1:3) == pmax(1:3, v1) & pmax(1:3, v1) == c(2,2,3)) [1] TRUE > all( pmin(v1, 1:3) == pmin(1:3, v1) & pmin(1:3, v1) == c(1,2,2)) [1] TRUE > > oo <- options(warn = -1)# These four lines each would give 3-4 warnings : > all( pmax(m1, 1:7) == pmax(1:7, m1) & pmax(1:7, m1) == c(2:4,4:7)) [1] TRUE > all( pmin(m1, 1:7) == pmin(1:7, m1) & pmin(1:7, m1) == c(1:3,3,3,3,2)) [1] TRUE > all( pmax(m2, 1:7) == pmax(1:7, m2) & pmax(1:7, m2) == pmax(1:7, m1)) [1] TRUE > all( pmin(m2, 1:7) == pmin(1:7, m2) & pmin(1:7, m2) == c(1:3,2,2,2,2)) [1] TRUE > options(oo) > > ## pretty() > stopifnot(pretty(1:15) == seq(0,16, by=2), + pretty(1:15, h=2) == seq(0,15, by=5), + pretty(1) == 0:1, + pretty(pi) == c(2,4), + pretty(pi, n=6) == 2:4, + pretty(pi, n=10) == 2:5, + pretty(pi, shr=.1)== c(3, 3.5)) > > ## gave infinite loop [R 0.64; Solaris], seealso PR#390 : > all(pretty((1-1e-5)*c(1,1+3*Meps), 7) == seq(0,1,len=3)) [1] TRUE > > n <- 1000 > x12 <- matrix(NA, 2,n); x12[,1] <- c(2.8,3) # Bug PR#673 > for(j in 1:2) x12[j, -1] <- round(rnorm(n-1), dig = rpois(n-1, lam=3.5) - 2) > for(i in 1:n) { + lp <- length(p <- pretty(x <- sort(x12[,i]))) + stopifnot(p[1] <= x[1] & x[2] <= p[lp], + all(x==0) || all.equal(p, rev(-pretty(-x)), tolerance = 10*Meps)) + } > > ## PR#741: > pi != (pi0 <- pi + 2*.Machine$double.eps) [1] TRUE > is.na(match(c(1,pi,pi0), pi)[3]) [1] TRUE > > ## PR#749: > all(is.na(c(NA && TRUE, TRUE && NA, NA && NA, + NA || FALSE,FALSE || NA, NA || NA))) [1] TRUE > > all((c(NA || TRUE, TRUE || NA, + !c(NA && FALSE,FALSE && NA)))) [1] TRUE > > > ## not sure what the point of this is: it gives mean(numeric(0)), that is NaN > (z <- mean(rep(NA_real_, 2), trim = .1, na.rm = TRUE)) [1] NaN > is.na(z) [1] TRUE > > ## Last Line: > cat('Time elapsed: ', proc.time() - .proctime00,'\n') Time elapsed: 0.677 0.028 0.714 0 0 >