findConjugates: Find complex conjugate pairs In FinTS: Companion to Tsay (2005) Analysis of Financial Time Series

Description

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

Usage

 `1` ```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(s)

`plotArmaTrueacf`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```# none findConjugates(NULL) findConjugates(numeric(0)) findConjugates(0:4) findConjugates(rep(0:1,each=3)) # some findConjugates(c(1+1i, 0, 1-1i, 2-2i, 3, 2+2i, NA)) # 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 } ```