Find complex conjugate pairs

Description

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

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)

Spencer Graves and Ravi Varadhan

See Also

plotArmaTrueacf

Examples

# 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
}

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(FinTS)
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FinTS/findConjugates.Rd_%03d_medium.png", width=480, height=480)
> ### Name: findConjugates
> ### Title: Find complex conjugate pairs
> ### Aliases: findConjugates
> ### Keywords: arith
> 
> ### ** 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
[1] -0.6273514-0.5454306i  0.2827538+0.8198364i -0.8116597-0.2088207i
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>