R: Check the Integral of r f_r(r)

checkintrfr {polyCub} | R Documentation

## Check the Integral of r f_r(r)

### Description

This function is auxiliary to `polyCub.iso`. The (analytical) integral of r f_r(r) from 0 to R is checked against a numeric approximation using `integrate` for various values of the upper bound R. A warning is issued if inconsistencies are found.

### Usage

    checkintrfr(intrfr, f, ..., center, control = list(), rs = numeric(0L),
      tolerance = control$rel.tol)

### Arguments

`intrfr` | a `function(R, ...)`, which implements the (analytical) antiderivative of r f_r(r) from 0 to `R`. The first argument must be vectorized but not necessarily named `R`. If `intrfr` is missing, it will be approximated numerically via `integrate(function(r, ...) r * f(cbind(x0 + r, y0), ...), 0, R, ..., control=control)`, where `c(x0, y0)` is the `center` of isotropy. Note that `f` will not be checked for isotropy.
`f` | a two-dimensional real-valued function. As its first argument it must take a coordinate matrix, i.e., a numeric matrix with two columns, and it must return a numeric vector of length the number of coordinates.
`...` | further arguments for `f` or `intrfr`.
`center` | numeric vector of length 2, the center of isotropy.
`control` | list of arguments passed to `integrate`, the quadrature rule used for the line integral along the polygon boundary.
`rs` | numeric vector of upper bounds for which to check the validity of `intrfr`. If it has length 0 (default), no checks are performed.
`tolerance` | of `all.equal.numeric` when comparing `intrfr` results with numerical integration. Defaults to the relative tolerance used for `integrate`.

### Value

The `intrfr` function. If it was not supplied, its quadrature version using `integrate` is returned.

[Package polyCub version 0.7.1 Index]