Numerical integration of continuously differentiable
functions f(x,y) over simple closed polygonal domains.
The following cubature methods are implemented:
product Gauss cubature (Sommariva and Vianello, 2007,
The R package polyCub implements cubature (numerical integration) over polygonal domains. It solves the problem of integrating a continuously differentiable function f(x,y) over simple closed polygons.
For the special case of a rectangular domain along the axes, the
cubature
package is more appropriate (cf.
CRAN Task View: Numerical Mathematics
).
You can install polyCub from CRAN via:
install.packages("polyCub")
To install the development version from the GitHub repository, use:
## install.packages("remotes")remotes::install_github("bastistician/polyCub")
The basic usage is:
library("polyCub")polyCub(polyregion, f)
polyregion
represents the integration domain as an object of class
"owin"
(from spatstat), "gpc.poly
" (from gpclib or rgeos),
or "SpatialPolygons"
(from sp),
or even as a plain list of lists of vertex coordinates ("xylist"
).
f
is the integrand and needs to take a two-column coordinate matrix
as its first argument.
The polyCub()
function by default calls polyCub.SV()
,
a C-implementation of product Gauss cubature.
The various implemented cubature methods can also be called directly.
polyCub.SV()
:
General-purpose product Gauss cubature
(Sommariva and Vianello, 2007, BIT Numerical Mathematics,
https://doi.org/10.1007/s10543-007-0131-2)
polyCub.midpoint()
:
Simple two-dimensional midpoint rule based on
spatstat::as.im.function()
polyCub.iso()
:
Adaptive cubature for radially symmetric functions
via line integrate()
along the polygon boundary
(Meyer and Held, 2014, The Annals of Applied Statistics,
https://doi.org/10.1214/14-AOAS743, Supplement B, Section 2.4)
polyCub.exact.Gauss()
:
Accurate (but slow) integration of the bivariate Gaussian density
based on polygon triangulation and
mvtnorm::pmvnorm()
For details and illustrations see the vignette("polyCub")
in the installed package or
on CRAN.
The polyCub package evolved from the need to integrate so-called spatial interaction functions (Gaussian or power-law kernels) over the observation region (an administrative shapefile) of a spatio-temporal point process. Such epidemic models are implemented in surveillance.
polyCub also powers phylogeographic analyses in rase.
Contributions are welcome!
Please submit suggestions or report bugs at
https://github.com/bastistician/polyCub/issues
or via e-mail to maintainer("polyCub")
.
Note that pull requests should only be submitted
after discussion of the underlying issue.
The polyCub package is free and open source software, licensed under the GPLv2.
Added a getting started vignette("polyCub")
(suggested by @wrathematics in
openjournals/joss-reviews#1056).
fix minor compiler warning about missing types
field in R_CMethodDef
(@wrathematics, #1).
Package polyCub no longer attaches package sp (moved from "Depends" to "Imports").
The R code of the examples is no longer installed by default.
Use the --example
flag of R CMD INSTALL to achieve that.
The README now exemplifies the four different cubature rules.
The exported C-function polyCub_iso()
...
did not handle its stop_on_error
argument correctly
(it would always stop on error).
now detects non-finite intrfr
function values and gives an
informative error message (rather than just reporting "abnormal
termination of integration routine").
Package polyCub no longer strictly depends on package
spatstat.
It is only required for polyCub.midpoint()
and for polygon input of
class "owin"
.
Added full C-implementation of polyCub.iso()
, which is exposed as
"polyCub_iso"
for use by other R packages (notably future versions of
surveillance)
via LinkingTo: polyCub
and #include <polyCubAPI.h>
.
Accommodate CRAN checks: add missing import from graphics, register native routines and disable symbol search
polyCub.midpoint()
works directly with input polygons of classes
"gpc.poly"
and "SpatialPolygons"
, since package polyCub now
registers corresponding as.owin
-methods.
polyCub.exact.Gauss()
did not work if the tristrip
of the
transformed input polygon contained degenerate triangles (spotted by
Ignacio Quintero).
Line integration in polyCub.iso()
could break due to division by zero
if the center
point was part of the polygon boundary.
Nodes and weights for polyCub.SV()
were only cached up to nGQ=59
,
not 60 as announced in version 0.5-0. Fixed that which also makes
examples truly run without statmod.
In polyCub.SV()
, the new special setting f=NULL
means to only
compute nodes and weights.
Internal changes to the "gpc.poly"
converters to accommodate
spatstat 1.39-0.
polyCub.SV()
gained an argument engine
to choose among available
implementations. The new and faster C-implementation is the default.
There should not be any numerical differences in the result of the
cubature.
Package statmod is no
longer strictly required (imported). Nodes and weights for
Gauss-Legendre quadrature in polyCub.SV()
are now cached in the
polyCub package up to nGQ=60
. statmod::gauss.quad
is only
queried for a higher number of nodes.
polyCub.iso()
...
could not handle additional arguments for integrate()
given in the
control
list.
now applies the control
arguments also to the numerical
approximation of intrfr
.
The checkintrfr()
function is exported and documented.
Added a CITATION file.
plotpolyf()
...
gained an additional argument print.args
, an optional list of
arguments passed to print.trellis()
if use.lattice=TRUE
.
passed a data frame of coordinates to f
instead of a matrix as
documented.
rgeos (and therefore the GEOS library) is no longer strictly required (moved from "Imports" to "Suggests").
Added coerce
-methods from "Polygons"
(or "SpatialPolygons"
or
"Polygon"
) to "owin"
(as(..., "owin")
).
S4-style coerce
-methods between "gpc.poly"
and "Polygons"
/"owin"
have been removed from the package (since we no longer import the formal
class "gpc.poly"
from gpclib or rgeos). However, there are two
new functions gpc2owin
and owin2gpc
similar to those dropped from
spatstat since
version 1.34-0.
Moved discpoly()
back to
surveillance
since it is only used there.
The latter two changes cause surveillance version 1.6-0 to be incompatible with this new version of polyCub. Appropriate modifications have been made in the new version 1.7-0 of surveillance.
polyCub.SV()
thorough optimization of polyCub.SV()
-related code resulted in about
27% speed-up:
use mapply()
instead of a for
-loop
avoid cbind()
use tcrossprod()
less object copying
xylist()
is now exported. It simply extracts polygon coordinates from
various spatial classes (with same unifying intention as xy.coords()
).
A polyregion
of class "SpatialPolygons"
of length more than 1 now
works in polyCub
-methods.
Use aspect ratio of 1 in plotpolyf()
.
R CMD check
in the current R development version (also import packages into
the NAMESPACE which are listed in the "Depends" field).New cubature method polyCub.iso()
specific to isotropic functions
(thanks to Emil Hedevang for the basic idea).
New function plotpolyf()
to plot a polygonal domain on top of an image
of a bivariate function.
The package now depends on R >= 2.15.0 (for .rowSums()
).
The package no longer registers "owin"
as an S4-class since we depend
on the sp package which does the job. This avoids a spurious warning
(in .simpleDuplicateClass()
) upon package installation.
In discpoly()
, the argument r
has been renamed to radius
. This is
backward compatible by partial argument matching in old code.
This is the initial version of the polyCub package mainly built on functions previously maintained within the surveillance package. These methods for cubature of polygonal domains have been outsourced into this separate polyCub package since they are of general use for other packages as well.
The polyCub package has more documentation and tests, avoids the use
of gpclib as far as
possible (using rgeos
instead), and solves a compatibility issue with package
maptools (use
setClass("owin")
instead of setOldClass("owin")
).