pgs-internal {pgs} | R Documentation |
Internal pgs functions. These functions should not be called by most users.
cubicgrid(s,d=2) dualmat(x) gaic(a,x) in.upper.halfspace(x) normphase(h,E,Einv=solve(E)) pointcov(x,tol=.Machine$double.eps ^ 0.5) sphereSurface(d=2) ellipsoidSurface(a)
s |
a list of vectors or a vector. |
d |
an integer, the space dimension. Default: 2. |
x |
an array, a matrix or a vector. |
a |
a numeric. |
h |
a vector or a matrix. |
E |
a matrix. |
Einv |
a matrix. |
tol |
a numeric. |
cubicgrid
computes the coordinates of the points of the
Cartesian product set s1 x...x sd where the si's are subsets of reals.
The si's may be provided as a list of vectors or a vector s
. In
the latter case, the vector s is replicated d-times in the list
list(s,...,s).
dualmat
computes the dual of a non-singular square matrix
x
.
gaic
computes the incomplete gamma function with parameter
a
for a vector or an array of reals x
.
in.upper.halfspace
is used to test if the vector x
is in
the upper half-space. Upper half-space: null vector or last non-zero
coordinate is greater than 0.
normphase
normalizes the vector h
with respect to a vector lattice. The lattice is defined by its
generating matrix E
. The normalized vector lies inside the
fundamental tile defined by E
and differs from h
by a
lattice vector. When h
is a matrix, the transformation is applied
to each column vector.
pointcov
computes the set S-S for a given finite set of
points S. The points are defined as the columns of a matrix
x
. The result is given as a list with two components ud
and n
. The component ud
contains the points of S-S lying
in the upper half-space (S-S is symmetric). The component n
provides multiplicities: n[i]
is the multiplicity of
ud[,i]
. The parameter tol
controls the precision level
in comparisons.
sphereSurface
computes the surface area of the unit sphere in the
d-dimensional space.
ellipsoidSurface
computes the surface area of an ellipsoid in a
space of arbitrary dimension. The argument a is a vector containing
the semi-axis lengths. The algorithm is based on Garry Tee (2005) Surface area and capacity of
ellipsoids in n dimensions. New Zealand Journal of Mathematics,
34(2), 165–198. It involves numerical one-dimensional integration.
cubicgrid(c(1,2,5)) dualmat(diag(1:2)) gaic(1.2,seq(0.5,10,length=10)) in.upper.halfspace(c(-1,0)) in.upper.halfspace(c(1,0)) normphase(c(1.8,1.5),diag(1:2)) pointcov(matrix(c(0,0,1,0,1,1,0,1,1/2,1/2),nrow=2)) sphereSurface(2)