checkintrfr

analytical antiderivative of \(r f_r(r)\) from 0 to <code>R</code>
(first argument, not necessarily named <code>&quot;R&quot;</code>, must be vectorized).
If missing, <code>intrfr</code> is approximated numerically using
<code><a rd-options="" href="/link/integrate?package=polyCub&version=0.5-2" data-mini-rdoc="polyCub::integrate">integrate</a></code> configured with <code>control</code>.

intrfr

a two-dimensional real 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 <code>f</code> or <code>intrfr</code>.

numeric vector of length 2, the center of isotropy.

center

list of arguments passed to <code><a rd-options="" href="/link/integrate?package=polyCub&version=0.5-2" data-mini-rdoc="polyCub::integrate">integrate</a></code>, the
quadrature rule used for the line integral along the polygon boundary.

control

numeric vector of upper bounds for which to check the validity of
<code>intrfr</code>. If it has length 0, no checks are performed.

of <code><a rd-options="" href="/link/all.equal.numeric?package=polyCub&version=0.5-2" data-mini-rdoc="polyCub::all.equal.numeric">all.equal.numeric</a></code> when comparing
<code>intrfr</code> results with numerical integration. Defaults to the
relative tolerance used for <code>integrate</code>.

tolerance

This function is auxiliary to <code><a rd-options="" href="/link/polyCub.iso?package=polyCub&version=0.5-2" data-mini-rdoc="polyCub::polyCub.iso">polyCub.iso</a></code>.
The (analytical) integral of \(r f_r(r)\) from 0 to \(R\) is checked
against a numeric approximation using <code><a rd-options="" href="/link/integrate?package=polyCub&version=0.5-2" data-mini-rdoc="polyCub::integrate">integrate</a></code> for various
values of the upper bound \(R\). A warning is issued if inconsistencies
are found.

The following methods for cubature (numerical integration)
over polygonal domains are currently implemented:
the two-dimensional midpoint rule as a simple wrapper around
as.im.function() from package spatstat (Baddeley and Turner, 2005),
the product Gauss cubature by Sommariva and Vianello (2007),
an adaptive cubature for isotropic functions via line integrate()
along the boundary (Meyer and Held, 2014),
and quasi-exact methods specific to the integration of the
bivariate Gaussian density over polygonal and circular domains
(based on formulae from the Abramowitz and Stegun (1972) handbook).
For cubature over simple hypercubes, the packages "cubature" and
"R2Cuba" are more appropriate.

Sebastian Meyer

polyCub

Cubature over Polygonal Domains

Leonhard Held

Michael Hoehle

checkintrfr function

analytical antiderivative of \(r f_r(r)\) from 0 to <code>R</code>
(first argument, not necessarily named <code>&quot;R&quot;</code>, must be vectorized).
If missing, <code>intrfr</code> is approximated numerically using
<code><a rd-options='' href='integrate'>integrate</a></code> configured with <code>control</code>.

list of arguments passed to <code><a rd-options='' href='integrate'>integrate</a></code>, the
quadrature rule used for the line integral along the polygon boundary.

of <code><a rd-options='' href='all.equal.numeric'>all.equal.numeric</a></code> when comparing
<code>intrfr</code> results with numerical integration. Defaults to the
relative tolerance used for <code>integrate</code>.

This function is auxiliary to <code><a rd-options='' href='polyCub.iso'>polyCub.iso</a></code>.
The (analytical) integral of \(r f_r(r)\) from 0 to \(R\) is checked
against a numeric approximation using <code><a rd-options='' href='integrate'>integrate</a></code> for various
values of the upper bound \(R\). A warning is issued if inconsistencies
are found.

checkintrfr: Check the Integral of

Description

Usage

Arguments

Value