SphericalMisc: Miscellaneous internal functions used by SphericalCubature...

In SphericalCubature: Numerical Integration over Spheres and Balls in n-Dimensions; Multivariate Polar Coordinates

Description

These functions are not intended for general use, they are only listed here to document their existence.

adaptIntegrateCheck is used by the adaptive integration functions to check input parameters, partitionRegion is used by the 'split' versions of the the adaptive integration functions, nextGraySubset is used by IntegrateSphereStroud11, nextMultiIndex is used by adaptive integration functions, nextBinary is used by Orthants.

Usage

adaptIntegrateSphereCheck( n, lowerLimit, upperLimit, R, xstar, width )
partitionRegion( xstar, width, lowerLimit, upperLimit )
nextGraySubset( gray.list )
nextMultiIndex( j, size )
CheckUnitVectors( S, eps=1.0e-14 )
Orthants( n, positive.only=FALSE )
SubdivideSphereTriByOrthant( S, eps=1.0e-14 )
nextBinary( b )

Arguments

n	dimension of the space
lowerLimit	lower angular limit for integration region
upperLimit	upper angular limit for integration region
R	inner and outer radii for integration region
xstar	directions where function changes rapidly
width	width of subdivisions
gray.list	list used by Stroud integration
j	current multi-index
size	length of multi-index
S	a matrix or array specifying simplices
eps	tolerance used in test for unit vectors
positive.only	logical; if TRUE, only the first orthant is returned, if FALSE, all 2^n orthants are returned
b	a vector of integers, representing a number in base 2

Details

Orthant() returns an array of simplices in the V representation; each one gives the points on the axes that are on the boundary of one orthant. CheckSphereTri() performs validity checks on the simplices in S.

SphericalCubature documentation built on Jan. 13, 2021, 1:04 p.m.