Find complex conjugate pairs

Find all complex conjugate pairs in a vector of complex numbers and return one number from each pair.

Usage

findConjugates(x, complex.eps = .Machine[["double.eps"]])

Arguments

x

a vector of complex numbers

complex.eps

a small positive number used to identify complex conjugates: x[i] and x[j] are considered conjugates if

(abs(x-Conj(x)) / max(abs(x[i], x[j]))) < complex.eps

and (abs(x[i] - x[j]) > complex.eps. The latter condition excludes repeated roots.

Details

1. Compute normalization m2 = outer(abs(x), abs(x), max).

2. Compute complex differences c2 = abs(outer(x, Conj(x), "-")) / m2.

3. If any abs(c2) < complex.eps, make sure the numbers are not duplicate reals via

(d2 = abs(outer(x, x, "-"))) > complex.eps.

Value

a complex vector with one representative of each complex pair found

Author

Spencer Graves and Ravi Varadhan

See also

plotArmaTrueacf

Examples

# none
findConjugates(NULL)
#> complex(0)
findConjugates(numeric(0))
#> complex(0)
findConjugates(0:4)
#> complex(0)
findConjugates(rep(0:1,each=3))
#> complex(0)

# some
findConjugates(c(1+1i, 0, 1-1i, 2-2i, 3, 2+2i, NA))
#> [1] 1-1i 2+2i

# Testing with polyroot and solve(polynomial(...))
set.seed(1234)
if(require(polynom)){
  p <- polynomial(sample(1:10, size=45, rep=TRUE)) # degree 44
  z <- solve(p)
  findConjugates(z, complex.eps=.Machine$double.eps)
  # this identifies all 21 conjugate pairs, R 2.6.0 for Windows

  z1 <- polyroot(p)
  findConjugates(z1, complex.eps=.Machine$double.eps)
  # this only identifies only 3 conjugate pairs, R 2.6.0 for Windows
}
#> Loading required package: polynom
#> complex(0)