checkUnitSphere: Domain check for unit sphere \{\vec{x} \in R^n : \Vert...

In multIntTestFunc: Provides Test Functions for Multivariate Integration

Domain check for unit sphere \{\vec{x} \in R^n : \Vert \vec{x} \Vert_{2} = 1\}

Description

The function checks if a point (one row in the input argument) is inside the unit sphere \{\vec{x} \in R^n : \Vert \vec{x} \Vert_2 = 1\} or not. If the input matrix contains entries that are not numeric, i.e., not representing real numbers, the function throws an error. The dimension n is automatically inferred from the input matrix and is equal to the number of columns. The function allows for an additional parameter \varepsilon\geq 0 to test \{\vec{x} \in R^n : 1-\varepsilon \leq \Vert \vec{x} \Vert_2 \leq 1 + \varepsilon\}. WARNING: Due to floating point arithmetic the default value of \varepsilon=0 will not work properly in most cases.

Usage

checkUnitSphere(x, eps = 0)

Arguments

x	Matrix with numeric entries. Each row represents one point
eps	Non-negative numeric that allows to test points with an additional tolerance

Value

Vector where each element (TRUE or FALSE) indicates if a point is in the unit sphere

Author(s)

Klaus Herrmann

Examples

x <- matrix(rnorm(30),10,3)
checkUnitSphere(x,eps=0.001)

multIntTestFunc documentation built on Sept. 11, 2024, 5:18 p.m.