fourierbasis {spatstat.geom} | R Documentation |
Fourier Basis Functions
Description
Evaluates the Fourier basis functions
on a d
-dimensional box
with d
-dimensional frequencies k_i
at the
d
-dimensional coordinates x_j
.
Usage
fourierbasis(x, k, win = boxx(rep(list(0:1), ncol(k))))
fourierbasisraw(x, k, boxlengths)
Arguments
x |
Coordinates.
A |
k |
Frequencies.
A |
win |
window (of class |
boxlengths |
numeric giving the side lengths of the box domain of the Fourier functions. |
Details
The result is an m
by n
matrix where the (i,j)
'th
entry is the d
-dimensional Fourier basis function with
frequency k_i
evaluated at the point x_j
, i.e.,
\frac{1}{\sqrt{|W|}}
\exp(2\pi i \sum{l=1}^d k_{i,l} x_{j,l}/L_l)
where L_l
, l=1,...,d
are the box side lengths
and |W|
is the volume of the
domain (window/box). Note that the algorithm does not check whether
the coordinates given in x
are contained in the given box.
Actually the box is only used to determine the side lengths and volume of the
domain for normalization.
The stripped down faster version fourierbasisraw
doesn't do checking or
conversion of arguments and requires x
and k
to be matrices.
Value
An m
by n
matrix of complex values.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
Rolf Turner rolfturner@posteo.net
and Ege Rubak rubak@math.aau.dk
Examples
## 27 rows of three dimensional Fourier frequencies:
k <- expand.grid(-1:1,-1:1, -1:1)
## Two random points in the three dimensional unit box:
x <- rbind(runif(3),runif(3))
## 27 by 2 resulting matrix:
v <- fourierbasis(x, k)
head(v)