Provides Test Functions for Multivariate Integration

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Documentation for package ‘multIntTestFunc’ version 0.2.0

• DESCRIPTION file.
• User guides, package vignettes and other documentation.

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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_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_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}