R: Provides Test Functions for Multivariate Integration

# Provides Test Functions for Multivariate Integration

## Documentation for package ‘multIntTestFunc’ version 0.3.0

- DESCRIPTION file
- User guides, package vignettes and other documentation
- Package NEWS

## Help Pages

checkClosedUnitBall | Domain check for closed unit ball \{\vec{x} \in R^n : \Vert \vec{x} \Vert_{2} <=q 1\}
checkClosedUnitCube | Domain check for closed unit hypercube [0,1]^n
checkPos | Domain check for [0,Inf)^n
checkRn | Domain check for R^n
checkStandardSimplex | Domain check for standard simplex \{\vec{x} \in R^n : x_i >=q 0, \Vert \vec{x} \Vert_1 <=q 1 \}
checkUnitSphere | Domain check for unit sphere \{\vec{x} \in R^n : \Vert \vec{x} \Vert_{2} = 1\}
domainCheck | Check if node points are in the domain of a test function instance
domainCheck-method | Check if node points are in the domain of a test function instance
domainCheckP | Check if node points are in the domain of a test function instance ("overload" of domainCheck with additional parameter)
domainCheckP-method | Check if node points are in the domain of a test function instance ("overload" of domainCheck with additional parameter)
evaluate | Evaluate test function instance for a set of node points
evaluate-method | Evaluate test function instance for a set of node points
exactIntegral | Get exact integral for test function instance
exactIntegral-method | Get exact integral for test function instance
getIntegrationDomain | Get description of integration domain for test function instance
getIntegrationDomain-method | Get description of integration domain for test function instance
getReferences | Get references for test function instance
getReferences-method | Get references for test function instance
getTags | Get tags for test function instance
getTags-method | Get tags for test function instance
multIntTestFunc | multIntTestFunc: A package to define test functions for multivariate numerical integration.
pIntRule | Product rule for numerical quadrature from univariate nodes and weights
Pn_lognormalDensity | An S4 class to represent the function \frac{1}{(prod_{i=1}^{n}x_i) sqrt{(2pi)^n\det(Sigma)}}\exp(-((\ln(\vec{x})-\vec{mu})^{T}Sigma^{-1}(\ln(\vec{x})-\vec{mu}))/2) on [0,Inf)^n
Pn_lognormalDensity-class | An S4 class to represent the function \frac{1}{(prod_{i=1}^{n}x_i) sqrt{(2pi)^n\det(Sigma)}}\exp(-((\ln(\vec{x})-\vec{mu})^{T}Sigma^{-1}(\ln(\vec{x})-\vec{mu}))/2) on [0,Inf)^n
Pn_logtDensity | An S4 class to represent the function (prod_{i=1}^n x_i^{-1})\frac{Gamma<=ft[(nu+n)/2\right]}{Gamma(nu/2)nu^{n/2}pi^{n/2}<=ft|{Sigma}\right|^{1/2}}<=ft[1+\frac{1}{nu}({\log(\vec{x})}-{\vec{delta}})^{T}{Sigma}^{-1}({\log(\vec{x})}-{\vec{delta}})\right]^{-(nu+n)/2} on [0,Inf)^n
Pn_logtDensity-class | An S4 class to represent the function (prod_{i=1}^n x_i^{-1})\frac{Gamma<=ft[(nu+n)/2\right]}{Gamma(nu/2)nu^{n/2}pi^{n/2}<=ft|{Sigma}\right|^{1/2}}<=ft[1+\frac{1}{nu}({\log(\vec{x})}-{\vec{delta}})^{T}{Sigma}^{-1}({\log(\vec{x})}-{\vec{delta}})\right]^{-(nu+n)/2} on [0,Inf)^n
Rn_floorNorm | An S4 class to represent the function \frac{Gamma(n/2+1)}{pi^{n/2}(1+\lfloor \Vert \vec{x} \Vert_2^n \rfloor)^s} on R^n
Rn_floorNorm-class | An S4 class to represent the function \frac{Gamma(n/2+1)}{pi^{n/2}(1+\lfloor \Vert \vec{x} \Vert_2^n \rfloor)^s} on R^n
Rn_Gauss | An S4 class to represent the function \exp(-\vec{x}\cdot\vec{x}) on R^n
Rn_Gauss-class | An S4 class to represent the function \exp(-\vec{x}\cdot\vec{x}) on R^n
Rn_normalDensity | An S4 class to represent the function \frac{1}{sqrt{(2pi)^n\det(Sigma)}}\exp(-((\vec{x}-\vec{mu})^{T}Sigma^{-1}(\vec{x}-\vec{mu}))/2) on R^n
Rn_normalDensity-class | An S4 class to represent the function \frac{1}{sqrt{(2pi)^n\det(Sigma)}}\exp(-((\vec{x}-\vec{mu})^{T}Sigma^{-1}(\vec{x}-\vec{mu}))/2) on R^n
Rn_tDensity | An S4 class to represent the function \frac{Gamma<=ft[(nu+n)/2\right]}{Gamma(nu/2)nu^{n/2}pi^{n/2}<=ft|{Sigma}\right|^{1/2}}<=ft[1+\frac{1}{nu}({\vec{x}}-{\vec{delta}})^{T}{Sigma}^{-1}({\vec{x}}-{\vec{delta}})\right]^{-(nu+n)/2} on R^n
Rn_tDensity-class | An S4 class to represent the function \frac{Gamma<=ft[(nu+n)/2\right]}{Gamma(nu/2)nu^{n/2}pi^{n/2}<=ft|{Sigma}\right|^{1/2}}<=ft[1+\frac{1}{nu}({\vec{x}}-{\vec{delta}})^{T}{Sigma}^{-1}({\vec{x}}-{\vec{delta}})\right]^{-(nu+n)/2} on R^n
standardSimplex_Dirichlet | An S4 class to represent the function prod_{i=1}^{n}x_i^{v_i-1}(1 - x_1 - ... - x_n)^{v_{n+1}-1} on T_n
standardSimplex_Dirichlet-class | An S4 class to represent the function prod_{i=1}^{n}x_i^{v_i-1}(1 - x_1 - ... - x_n)^{v_{n+1}-1} on T_n
standardSimplex_exp_sum | An S4 class to represent the function \exp(-c(x_1 + ... + x_n)) on T_n
standardSimplex_exp_sum-class | An S4 class to represent the function \exp(-c(x_1 + ... + x_n)) on T_n
unitBall_normGauss | An S4 class to represent the function \frac{1}{(2pi)^{n/2}}\exp(-\Vert\vec{x}\Vert_2^2/2) on B^{n}
unitBall_normGauss-class | An S4 class to represent the function \frac{1}{(2pi)^{n/2}}\exp(-\Vert\vec{x}\Vert_2^2/2) on B^{n}
unitBall_polynomial | An S4 class to represent the function prod_{i=1}^n x_i^{a_i} on B_n
unitBall_polynomial-class | An S4 class to represent the function prod_{i=1}^n x_i^{a_i} on B_n
unitCube_BFN1 | An S4 class to represent the function prod^{n}_{i=1}\vert 4x_i-2\vert on [0,1]^n
unitCube_BFN1-class | An S4 class to represent the function prod^{n}_{i=1}\vert 4x_i-2\vert on [0,1]^n
unitCube_BFN2 | An S4 class to represent the function prod^{n}_{i=1} i\cos(ix_i) on [0,1]^n
unitCube_BFN2-class | An S4 class to represent the function prod^{n}_{i=1} i\cos(ix_i) on [0,1]^n
unitCube_BFN3 | An S4 class to represent the function prod^{n}_{i=1} T_{nu(i)}(2x_i-1) on [0,1]^n
unitCube_BFN3-class | An S4 class to represent the function prod^{n}_{i=1} T_{nu(i)}(2x_i-1) on [0,1]^n
unitCube_BFN4 | An S4 class to represent the function sum_{i=1}^{n}(-1)^i prod_{j=1}^{i} x_j on [0,1]^n
unitCube_BFN4-class | An S4 class to represent the function sum_{i=1}^{n}(-1)^i prod_{j=1}^{i} x_j on [0,1]^n
unitCube_cos2 | An S4 class to represent the function (\cos(\vec{x}\cdot\vec{v}))^2 on [0,1]^n
unitCube_cos2-class | An S4 class to represent the function (\cos(\vec{x}\cdot\vec{v}))^2 on [0,1]^n
unitCube_floor | An S4 class to represent the function \lfloor x_1 + ... + x_n \rfloor on [0,1]^n
unitCube_floor-class | An S4 class to represent the function \lfloor x_1 + ... + x_n \rfloor on [0,1]^n
unitCube_Genz1 | An S4 class to represent the function \cos<=ft(2pi u + sum^{n}_{i=1} a_i x_i \right) on [0,1]^n
unitCube_Genz1-class | An S4 class to represent the function \cos<=ft(2pi u + sum^{n}_{i=1} a_i x_i \right) on [0,1]^n
unitCube_max | An S4 class to represent the function \max(x_1,...,x_n) on [0,1]^n
unitCube_max-class | An S4 class to represent the function \max(x_1,...,x_n) on [0,1]^n
unitSphere_innerProduct1 | An S4 class to represent the function (\vec{x}\cdot\vec{a})(\vec{x}\cdot\vec{b}) on S^{n-1}
unitSphere_innerProduct1-class | An S4 class to represent the function (\vec{x}\cdot\vec{a})(\vec{x}\cdot\vec{b}) on S^{n-1}
unitSphere_polynomial | An S4 class to represent the function prod_{i=1}^n x_i^{a_i} on S^{n-1}
unitSphere_polynomial-class | An S4 class to represent the function prod_{i=1}^n x_i^{a_i} on S^{n-1}