findq.Rmd

---
title: "Polynomial roots in (0,1)"
author: "Douglas Bates"
date: "09/05/2014"
output: html_document
---

# Finding roots in the unit interval

Instead of using the `polyroot` function I would use the `polynom` package, written by Bill Venables and now maintained by Kurt Hornik and Martin Maechler.
```{r library}
library(polynom)
(p <- polynomial(c(0.1, 0.3, 0.4, 0.0,0.2)))
```
To scale the coefficients so that they add to 1, you don't compare with 1.  You use
```{r compare}
all.equal(sum(as.vector(p)),1)
```

In general you should use tolerances based on the "relative machine precision", which is available as
```{r eps}
.Machine$double.eps
```

For the general function you have
```{r findq}
findq <- function(pvector) {
    stopifnot(is.vector(pvector,"numeric"),
              all(pvector >= 0.))
    if (!isTRUE(all.equal(sum(pvector),1))) {
        ## do something here
    }
    roots <- solve(polynomial(pvector)-polynomial(c(0,1)))
    realroots <- Re(roots[which(abs(Im(roots)) < 1e3*.Machine$double.eps)])
    eligible <- realroots[0 <= realroots & realroots < 1]
    if (length(eligible) <= 1L) return(eligible)
    eligible[which.min(abs(eligible-0.5))]
}
```

Check out the function
```{r check}
findq(c(0.1, 0.3, 0.4, 0, 0.2))
```