R: Various utilities

is.nonpos {hypergeo} | R Documentation

## Various utilities

### Description

Various utilities needing nonce functions

### Usage

    is.near_integer(i, tol=getOption("tolerance"))
    is.nonpos(i)
    is.zero(i)
    isgood(x, tol)
    thingfun(z, complex=FALSE)
    crit(...)
    lpham(x,n)

### Arguments

`i` | Numerical vector of suspected integers
`tol` | Tolerance
`x` | Argument to `isgood()` and `lpham()`
`z` | Complex vector
`complex` | In function `thingfun()`, Boolean with default `FALSE` meaning to return the modulus of the transforms and `TRUE` meaning to return the complex values themselves
`n` | second argument to `lpham()`
`...` | Ignored

### Details

- Function `is.near_integer(i)` returns `TRUE` if `i` is “near” [that is, within `tol`] an integer; if the option is unset then `1e-11` is used.

- Function `is.nonpos()` returns `TRUE` if `i` is near a nonpositive integer

- Function `is.zero()` returns `TRUE` if `i` is, er, near zero

- Function `isgood()` checks for all elements of `x` having absolute values less than `tol`

- Function `thingfun()` transforms input vector `z` by each of the six members of the anharmonic group, viewed as a subgroup of the Mobius group of functions. It returns a real six-column matrix with columns being the modulus of z,z/(z-1),1-z,1/z,1/(1-z),1-1/z. These six columns correspond to the primary argument in equations 15.3.3 to 15.3.9, p551 of AMS-55

- Function `crit()` returns the two critical points, 1/2 +/- sqrt(3)i/2. These points have unit modulus as do their six transforms by `thingfun()`

- Function `lpham()` returns the log of the Pochhammer function log(Gamma(x+n)/Gamma(x))

### Note

Function `isgood()` uses zero as the default tolerance (argument `tol` passed in from `hypergeo()`); compare the different meaning of `tol` used in `is.near_integer()`.

Here, “integer” means one of the sequence 0, +/-1, +/-2, ... [ie not the Gaussian integers].

### Author(s)

Robin K. S. Hankin

### Examples

    is.near_integer(-3)

    is.zero(4)

[Package hypergeo version 1.2-13 Index]