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 ####=== 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 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 ##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) is.infinite( i1) & is.infinite( i2) & i1 > 12 & i2 > 12 is.infinite(-i1) & is.infinite(-i2) & (-i1) < -12 & (-i2) < -12 is.nan(n1 <- 0 / 0) is.nan( - n1) i1 == i1 + i1 i1 == i1 * i1 is.nan(i1 - i1) is.nan(i1 / i1) 1/0 == Inf & 0 ^ -1 == Inf 1/Inf == 0 & Inf ^ -1 == 0 iNA <- as.integer(NA) !is.na(Inf) & !is.nan(Inf) & is.infinite(Inf) & !is.finite(Inf) !is.na(-Inf)& !is.nan(-Inf)& is.infinite(-Inf)& !is.finite(-Inf) is.na(NA) & !is.nan(NA) & !is.infinite(NA) & !is.finite(NA) is.na(NaN) & is.nan(NaN) & !is.infinite(NaN) & !is.finite(NaN) is.na(iNA) & !is.nan(iNA) & !is.infinite(iNA) & !is.finite(iNA) ## These are "double"s: all(!is.nan(c(1.,NA))) all(c(FALSE,TRUE,FALSE) == is.nan(c (1.,NaN,NA))) all(c(FALSE,TRUE,FALSE) == is.nan(list(1.,NaN,NA))) ## log() and "pow()" -- POSIX is not specific enough.. log(0) == -Inf is.nan(log(-1))# TRUE and warning rp <- c(1:2,Inf); rn <- rev(- rp) r <- c(rn, 0, rp) all(r^0 == 1) all((rn ^ -3) == -((-rn) ^ -3)) # all(c(1.1,2,Inf) ^ Inf == Inf) all(c(1.1,2,Inf) ^ -Inf == 0) .9 ^ Inf == 0 .9 ^ -Inf == Inf ## Wasn't ok in 0.64: all(1^c(-Inf,Inf) == 1) all(is.nan(rn ^ .5))# in some C's : (-Inf) ^ .5 gives Inf, instead of NaN ## Real Trig.: cos(0) == 1 sin(3*pi/2) == cos(pi) x <- rnorm(99) all( sin(-x) == - sin(x)) all( cos(-x) == cos(x)) x <- 1:99/100 all(abs(1 - x / asin(sin(x))) <= 2*Meps)# "== 2*" for HP-UX all(abs(1 - x / atan(tan(x))) < 2*Meps) ## 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 r <- rlnorm(5000) # NB random, and next has failed for some seed all(abs(rErr(gamma(r+1), r*gamma(r))) < 500 * Meps) ## 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 n <- 50; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 20*Meps)#Lnx: f=2 n <- 120; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 1000*Meps) n <- 10000;all(abs(rErr(lgamma(1:n),cumsum(log(c(1,1:(n-1)))))) < 100*Meps) n <- 10; all( gamma(1:n) == cumprod(c(1,1:(n-1)))) n <- 20; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 100*Meps) n <- 120; all(abs(rErr( gamma(1:n), cumprod(c(1,1:(n-1))))) < 1000*Meps) n <- 10000;all(abs(rErr(lgamma(1:n),cumsum(log(c(1,1:(n-1)))))) < 100*Meps) all(is.nan(gamma(0:-47))) # + warn. ## choose() {and lchoose}: n51 <- c(196793068630200, 229591913401900, 247959266474052) abs(c(n51, rev(n51))- choose(51, 23:28)) <= 2 all(choose(0:4,2) == c(0,0,1,3,6)) ## 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 all.equal(digamma(1) - digamma(1/2), log(4), tol=32*Meps)# Linux: < 1*Meps! n <- 1:12 all.equal(digamma(n), - gEuler + c(0, cumsum(1/n)[-length(n)]),tol=32*Meps)#i386 Lx: 1.3 Meps all.equal(digamma(n + 1/2), - gEuler - log(4) + 2*cumsum(1/(2*n-1)),tol=32*Meps)#i386 Lx: 1.8 Meps ## higher psigamma: all.equal(psigamma(1, deriv=c(1,3,5)), pi^(2*(1:3)) * c(1/6, 1/15, 8/63), tol=32*Meps) 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), 2*Meps), all.equal(trigamma(x), psigamma(x,1), 2*Meps))# TRUE (+ NaN warnings) ## 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 ## 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), tol = 20*Meps))# use tol=0 to see rel.error ## 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)) all( pmin(v1, 1:3) == pmin(1:3, v1) & pmin(1:3, v1) == c(1,2,2)) 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)) all( pmin(m1, 1:7) == pmin(1:7, m1) & pmin(1:7, m1) == c(1:3,3,3,3,2)) all( pmax(m2, 1:7) == pmax(1:7, m2) & pmax(1:7, m2) == pmax(1:7, m1)) all( pmin(m2, 1:7) == pmin(1:7, m2) & pmin(1:7, m2) == c(1:3,2,2,2,2)) 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)) 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)), tol = 10*Meps)) } ## PR#741: pi != (pi0 <- pi + 2*.Machine\$double.eps) is.na(match(c(1,pi,pi0), pi)[3]) ## PR#749: all(is.na(c(NA && TRUE, TRUE && NA, NA && NA, NA || FALSE,FALSE || NA, NA || NA))) all((c(NA || TRUE, TRUE || NA, !c(NA && FALSE,FALSE && NA)))) ## 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)) is.na(z) ## Last Line: cat('Time elapsed: ', proc.time() - .proctime00,'\n')
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