The R Project SVN R

### Tests of complex arithemetic.

Meps <- .Machine$double.eps

## complex

z <- 0i ^ (-3:3)

stopifnot(Re(z) == 0 ^ (-3:3))

## powers, including complex ones

a <- -4:12

m <- outer(a +0i, b <- seq(-.5,2, by=.5), "^")

dimnames(m) <- list(paste(a), "^" = sapply(b,format))

round(m,3)

stopifnot(m[,as.character(0:2)] == cbind(1,a,a*a),

                                        # latter were only approximate

          all.equal(unname(m[,"0.5"]),

                    sqrt(abs(a))*ifelse(a < 0, 1i, 1),

                    tolerance = 20*Meps))

## 2.10.0-2.12.1 got z^n wrong in the !HAVE_C99_COMPLEX case

z <- 0.2853725+0.3927816i

z2 <- z^(1:20)

z3 <- z^-(1:20)

z0 <- cumprod(rep(z, 20))

stopifnot(all.equal(z2, z0), all.equal(z3, 1/z0))

## was z^3 had value z^2 ....

## fft():

for(n in 1:30) cat("\nn=",n,":", round(fft(1:n), 8),"\n")

## polyroot():

stopifnot(abs(1 + polyroot(choose(8, 0:8))) < 1e-10)# maybe smaller..

## precision of complex numbers

signif(1.678932e80+0i, 5)

signif(1.678932e-300+0i, 5)

signif(1.678932e-302+0i, 5)

signif(1.678932e-303+0i, 5)

signif(1.678932e-304+0i, 5)

signif(1.678932e-305+0i, 5)

signif(1.678932e-306+0i, 5)

signif(1.678932e-307+0i, 5)

signif(1.678932e-308+0i, 5)

signif(1.678932-1.238276i, 5)

signif(1.678932-1.238276e-1i, 5)

signif(1.678932-1.238276e-2i, 5)

signif(1.678932-1.238276e-3i, 5)

signif(1.678932-1.238276e-4i, 5)

signif(1.678932-1.238276e-5i, 5)

signif(8.678932-9.238276i, 5)

## prior to 2.2.0 rounded real and imaginary parts separately.

## Complex Trig.:

abs(Im(cos(acos(1i))) -	 1) < 2*Meps

abs(Im(sin(asin(1i))) -	 1) < 2*Meps

##P (1 - Im(sin(asin(Ii))))/Meps

##P (1 - Im(cos(acos(Ii))))/Meps

abs(Im(asin(sin(1i))) -	 1) < 2*Meps

all.equal(cos(1i), cos(-1i)) # i.e. Im(acos(*)) gives + or - 1i:

abs(abs(Im(acos(cos(1i)))) - 1) < 4*Meps

set.seed(123) # want reproducible output

Isi <- Im(sin(asin(1i + rnorm(100))))

all(abs(Isi-1) < 100* Meps)

##P table(2*abs(Isi-1)	/ Meps)

Isi <- Im(cos(acos(1i + rnorm(100))))

all(abs(Isi-1) < 100* Meps)

##P table(2*abs(Isi-1)	/ Meps)

Isi <- Im(atan(tan(1i + rnorm(100)))) #-- tan(atan(..)) does NOT work (Math!)

all(abs(Isi-1) < 100* Meps)

##P table(2*abs(Isi-1)	/ Meps)

set.seed(123)

z <- complex(real = rnorm(100), imag = rnorm(100))

stopifnot(Mod ( 1 -  sin(z) / ( (exp(1i*z)-exp(-1i*z))/(2*1i) )) < 20 * Meps)

## end of moved from complex.Rd

## PR#7781

## This is not as given by e.g. glibc on AMD64

(z <- tan(1+1000i)) # 0+1i from R's own code.

stopifnot(is.finite(z))

##

## Branch cuts in complex inverse trig functions

atan(2)

atan(2+0i)

tan(atan(2+0i))

## should not expect exactly 0i in result

round(atan(1.0001+0i), 7)

round(atan(0.9999+0i), 7)

## previously not as in Abramowitz & Stegun.

## typo in z_atan2.

(z <- atan2(0+1i, 0+0i))

stopifnot(all.equal(z, pi/2+0i))

## was NA in 2.1.1

## Hyperbolic

x <- seq(-3, 3, len=200)

Meps <- .Machine$double.eps

stopifnot(

 Mod(cosh(x) - cos(1i*x))	< 20*Meps,

 Mod(sinh(x) - sin(1i*x)/1i)	< 20*Meps

)

## end of moved from Hyperbolic.Rd

## values near and on branch cuts

options(digits=5)

z <- c(2+0i, 2-0.0001i, -2+0i, -2+0.0001i)

asin(z)

acos(z)

atanh(z)

z <- c(0+2i, 0.0001+2i, 0-2i, -0.0001i-2i)

asinh(z)

acosh(z)

atan(z)

## According to C99, should have continuity from the side given if there

## are not signed zeros.

## Both glibc 2.12 and macOS 10.6 used continuity from above in the first set

## but they seem to assume signed zeros.

## Windows gave incorrect (NaN) values on the cuts.

stopifnot(identical(tanh(356+0i), 1+0i))

## Used to be NaN+0i on Windows

## Not a regression test, but rather one of the good cases:

(cNaN <- as.complex("NaN"))

stopifnot(identical(cNaN, complex(re = NaN)), is.nan(Re(cNaN)), Im(cNaN) == 0)

dput(cNaN) ## (real = NaN, imaginary = 0)

## Partly new behavior:

(c0NaN  <- complex(real=0, im=NaN))

(cNaNaN <- complex(re=NaN, im=NaN))

stopifnot(identical(cNaN, as.complex(NaN)),

          identical(vapply(c(cNaN, c0NaN, cNaNaN), format, ""),

                    c("NaN+0i", "0+NaNi", "NaN+NaNi")),

          identical(cNaN, NaN + 0i),

          identical(cNaN, Conj(cNaN)),

          identical(cNaN, cNaN+cNaN),

          identical(cNaNaN, 1i * NaN),

          identical(cNaNaN, complex(modulus= NaN)),

          identical(cNaNaN, complex(argument= NaN)),

          identical(cNaNaN, complex(arg=NaN, mod=NaN)),

          identical(c0NaN, c0NaN+c0NaN), # !

          ## Platform dependent, not TRUE e.g. on F21 gcc 4.9.2:

          ## identical(NA_complex_, NaN + NA_complex_ ) ,

          ## Probably TRUE, but by a standard ??

          ## identical(cNaNaN, 2 * c0NaN), # C-library arithmetic

          ## identical(cNaNaN, 2 * cNaN),  # C-library arithmetic

          ## identical(cNaNaN, NA_complex_ * Inf),

          TRUE)