Description Usage Arguments Details Examples

Internal pgs functions. These functions should not be called by most users.

1 2 3 4 5 6 7 8 | ```
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.

1 2 3 4 5 6 7 8 |

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