SphericalMisc function

Miscellaneous internal functions used by SphericalCubature package.

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.

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.