is.nonpos: Various utilities
In RobinHankin/hypergeo: The Gauss Hypergeometric Function

is.nonpos

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, \frac{1}{2}\pm\frac{\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\left(\Gamma(x+n)/\Gamma(x)\right)

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,\pm 1,\pm 2,\ldots [ie not the Gaussian integers].