Package: multIntTestFunc 0.3.0

Klaus Herrmann

multIntTestFunc: Provides Test Functions for Multivariate Integration

Provides implementations of functions that can be used to test multivariate integration routines. The package covers six different integration domains (unit hypercube, unit ball, unit sphere, standard simplex, non-negative real numbers and R^n). For each domain several functions with different properties (smooth, non-differentiable, ...) are available. The functions are available in all dimensions n >= 1. For each function the exact value of the integral is known and implemented to allow testing the accuracy of multivariate integration routines. Details on the available test functions can be found at on the development website.

Authors:Klaus Herrmann [aut, cre]

multIntTestFunc_0.3.0.tar.gz
multIntTestFunc_0.3.0.zip(r-4.5)multIntTestFunc_0.3.0.zip(r-4.4)multIntTestFunc_0.3.0.zip(r-4.3)
multIntTestFunc_0.3.0.tgz(r-4.4-any)multIntTestFunc_0.3.0.tgz(r-4.3-any)
multIntTestFunc_0.3.0.tar.gz(r-4.5-noble)multIntTestFunc_0.3.0.tar.gz(r-4.4-noble)
multIntTestFunc_0.3.0.tgz(r-4.4-emscripten)multIntTestFunc_0.3.0.tgz(r-4.3-emscripten)
multIntTestFunc.pdf |multIntTestFunc.html✨
multIntTestFunc/json (API)
NEWS

# Install 'multIntTestFunc' in R:
install.packages('multIntTestFunc', repos = c('https://klausherrmann.r-universe.dev', 'https://cloud.r-project.org'))

Peer review:

Bug tracker:https://github.com/klausherrmann/multinttestfunc/issues

On CRAN:

4.30 score 1 scripts 205 downloads 34 exports 2 dependencies

Last updated 3 months agofrom:14ec16c309. Checks:OK: 7. Indexed: yes.

TargetResultDate
Doc / VignettesOKNov 08 2024
R-4.5-winOKNov 08 2024
R-4.5-linuxOKNov 08 2024
R-4.4-winOKNov 08 2024
R-4.4-macOKNov 08 2024
R-4.3-winOKNov 08 2024
R-4.3-macOKNov 08 2024

Exports:checkClosedUnitBallcheckClosedUnitCubecheckPoscheckRncheckStandardSimplexcheckUnitSpheredomainCheckdomainCheckPevaluateexactIntegralgetIntegrationDomaingetReferencesgetTagspIntRulePn_lognormalDensityPn_logtDensityRn_floorNormRn_GaussRn_normalDensityRn_tDensitystandardSimplex_DirichletstandardSimplex_exp_sumunitBall_normGaussunitBall_polynomialunitCube_BFN1unitCube_BFN2unitCube_BFN3unitCube_BFN4unitCube_cos2unitCube_floorunitCube_Genz1unitCube_maxunitSphere_innerProduct1unitSphere_polynomial

Dependencies:mvtnormpracma

Integration Test for Rn

Rendered fromIntegration_Test_Rn.Rmdusingknitr::rmarkdownon Nov 08 2024.

Last update: 2023-04-18
Started: 2023-04-18

Monte Carlo Integration Tests for the Unit Hypercube

Rendered fromMC_Integration_Test_Unit_Hypercube.Rmdusingknitr::rmarkdownon Nov 08 2024.

Last update: 2023-04-18
Started: 2021-10-04

Readme and manuals

Help Manual

Help pageTopics
Domain check for closed unit ball \{\vec{x} \in R^n : \Vert \vec{x} \Vert_{2} <=q 1\}checkClosedUnitBall
Domain check for closed unit hypercube [0,1]^ncheckClosedUnitCube
Domain check for [0,Inf)^ncheckPos
Domain check for R^ncheckRn
Domain check for standard simplex \{\vec{x} \in R^n : x_i >=q 0, \Vert \vec{x} \Vert_1 <=q 1 \}checkStandardSimplex
Domain check for unit sphere \{\vec{x} \in R^n : \Vert \vec{x} \Vert_{2} = 1\}checkUnitSphere
Check if node points are in the domain of a test function instancedomainCheck domainCheck,Pn_lognormalDensity,matrix-method domainCheck,Pn_logtDensity,matrix-method domainCheck,Rn_floorNorm,matrix-method domainCheck,Rn_Gauss,matrix-method domainCheck,Rn_normalDensity,matrix-method domainCheck,Rn_tDensity,matrix-method domainCheck,standardSimplex_Dirichlet,matrix-method domainCheck,standardSimplex_exp_sum,matrix-method domainCheck,unitBall_normGauss,matrix-method domainCheck,unitBall_polynomial,matrix-method domainCheck,unitCube_BFN1,matrix-method domainCheck,unitCube_BFN2,matrix-method domainCheck,unitCube_BFN3,matrix-method domainCheck,unitCube_BFN4,matrix-method domainCheck,unitCube_cos2,matrix-method domainCheck,unitCube_floor,matrix-method domainCheck,unitCube_Genz1,matrix-method domainCheck,unitCube_max,matrix-method domainCheck,unitSphere_innerProduct1,matrix-method domainCheck,unitSphere_polynomial,matrix-method
Check if node points are in the domain of a test function instance ("overload" of domainCheck with additional parameter)domainCheckP domainCheckP,unitSphere_innerProduct1,matrix,list-method domainCheckP,unitSphere_polynomial,matrix,list-method
Evaluate test function instance for a set of node pointsevaluate evaluate,Pn_lognormalDensity,matrix-method evaluate,Pn_logtDensity,ANY-method evaluate,Rn_floorNorm,matrix-method evaluate,Rn_Gauss,matrix-method evaluate,Rn_normalDensity,matrix-method evaluate,Rn_tDensity,ANY-method evaluate,standardSimplex_Dirichlet,matrix-method evaluate,standardSimplex_exp_sum,matrix-method evaluate,unitBall_normGauss,matrix-method evaluate,unitBall_polynomial,matrix-method evaluate,unitCube_BFN1,matrix-method evaluate,unitCube_BFN2,matrix-method evaluate,unitCube_BFN3,matrix-method evaluate,unitCube_BFN4,matrix-method evaluate,unitCube_cos2,matrix-method evaluate,unitCube_floor,matrix-method evaluate,unitCube_Genz1,matrix-method evaluate,unitCube_max,matrix-method evaluate,unitSphere_innerProduct1,matrix-method evaluate,unitSphere_polynomial,matrix-method
Get exact integral for test function instanceexactIntegral exactIntegral,Pn_lognormalDensity-method exactIntegral,Pn_logtDensity-method exactIntegral,Rn_floorNorm-method exactIntegral,Rn_Gauss-method exactIntegral,Rn_normalDensity-method exactIntegral,Rn_tDensity-method exactIntegral,standardSimplex_Dirichlet-method exactIntegral,standardSimplex_exp_sum-method exactIntegral,unitBall_normGauss-method exactIntegral,unitBall_polynomial-method exactIntegral,unitCube_BFN1-method exactIntegral,unitCube_BFN2-method exactIntegral,unitCube_BFN3-method exactIntegral,unitCube_BFN4-method exactIntegral,unitCube_cos2-method exactIntegral,unitCube_floor-method exactIntegral,unitCube_Genz1-method exactIntegral,unitCube_max-method exactIntegral,unitSphere_innerProduct1-method exactIntegral,unitSphere_polynomial-method
Get description of integration domain for test function instancegetIntegrationDomain getIntegrationDomain,Pn_lognormalDensity-method getIntegrationDomain,Pn_logtDensity-method getIntegrationDomain,Rn_floorNorm-method getIntegrationDomain,Rn_Gauss-method getIntegrationDomain,Rn_normalDensity-method getIntegrationDomain,Rn_tDensity-method getIntegrationDomain,standardSimplex_Dirichlet-method getIntegrationDomain,standardSimplex_exp_sum-method getIntegrationDomain,unitBall_normGauss-method getIntegrationDomain,unitBall_polynomial-method getIntegrationDomain,unitCube_BFN1-method getIntegrationDomain,unitCube_BFN2-method getIntegrationDomain,unitCube_BFN3-method getIntegrationDomain,unitCube_BFN4-method getIntegrationDomain,unitCube_cos2-method getIntegrationDomain,unitCube_floor-method getIntegrationDomain,unitCube_Genz1-method getIntegrationDomain,unitCube_max-method getIntegrationDomain,unitSphere_innerProduct1-method getIntegrationDomain,unitSphere_polynomial-method
Get references for test function instancegetReferences getReferences,Pn_lognormalDensity-method getReferences,Pn_logtDensity-method getReferences,Rn_floorNorm-method getReferences,Rn_Gauss-method getReferences,Rn_normalDensity-method getReferences,Rn_tDensity-method getReferences,standardSimplex_Dirichlet-method getReferences,standardSimplex_exp_sum-method getReferences,unitBall_normGauss-method getReferences,unitBall_polynomial-method getReferences,unitCube_BFN1-method getReferences,unitCube_BFN2-method getReferences,unitCube_BFN3-method getReferences,unitCube_BFN4-method getReferences,unitCube_cos2-method getReferences,unitCube_floor-method getReferences,unitCube_Genz1-method getReferences,unitCube_max-method getReferences,unitSphere_innerProduct1-method getReferences,unitSphere_polynomial-method
Get tags for test function instancegetTags getTags,Pn_lognormalDensity-method getTags,Pn_logtDensity-method getTags,Rn_floorNorm-method getTags,Rn_Gauss-method getTags,Rn_normalDensity-method getTags,Rn_tDensity-method getTags,standardSimplex_Dirichlet-method getTags,standardSimplex_exp_sum-method getTags,unitBall_normGauss-method getTags,unitBall_polynomial-method getTags,unitCube_BFN1-method getTags,unitCube_BFN2-method getTags,unitCube_BFN3-method getTags,unitCube_BFN4-method getTags,unitCube_cos2-method getTags,unitCube_floor-method getTags,unitCube_Genz1-method getTags,unitCube_max-method getTags,unitSphere_innerProduct1-method getTags,unitSphere_polynomial-method
multIntTestFunc: A package to define test functions for multivariate numerical integration.multIntTestFunc
Product rule for numerical quadrature from univariate nodes and weightspIntRule
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)^nPn_lognormalDensity Pn_lognormalDensity-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)^nPn_logtDensity Pn_logtDensity-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^nRn_floorNorm Rn_floorNorm-class
An S4 class to represent the function \exp(-\vec{x}\cdot\vec{x}) on R^nRn_Gauss Rn_Gauss-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^nRn_normalDensity Rn_normalDensity-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^nRn_tDensity Rn_tDensity-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_nstandardSimplex_Dirichlet standardSimplex_Dirichlet-class
An S4 class to represent the function \exp(-c(x_1 + ... + x_n)) on T_nstandardSimplex_exp_sum standardSimplex_exp_sum-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_normGauss unitBall_normGauss-class
An S4 class to represent the function prod_{i=1}^n x_i^{a_i} on B_nunitBall_polynomial unitBall_polynomial-class
An S4 class to represent the function prod^{n}_{i=1}\vert 4x_i-2\vert on [0,1]^nunitCube_BFN1 unitCube_BFN1-class
An S4 class to represent the function prod^{n}_{i=1} i\cos(ix_i) on [0,1]^nunitCube_BFN2 unitCube_BFN2-class
An S4 class to represent the function prod^{n}_{i=1} T_{nu(i)}(2x_i-1) on [0,1]^nunitCube_BFN3 unitCube_BFN3-class
An S4 class to represent the function sum_{i=1}^{n}(-1)^i prod_{j=1}^{i} x_j on [0,1]^nunitCube_BFN4 unitCube_BFN4-class
An S4 class to represent the function (\cos(\vec{x}\cdot\vec{v}))^2 on [0,1]^nunitCube_cos2 unitCube_cos2-class
An S4 class to represent the function \lfloor x_1 + ... + x_n \rfloor on [0,1]^nunitCube_floor unitCube_floor-class
An S4 class to represent the function \cos<=ft(2pi u + sum^{n}_{i=1} a_i x_i \right) on [0,1]^nunitCube_Genz1 unitCube_Genz1-class
An S4 class to represent the function \max(x_1,...,x_n) on [0,1]^nunitCube_max unitCube_max-class
An S4 class to represent the function (\vec{x}\cdot\vec{a})(\vec{x}\cdot\vec{b}) on S^{n-1}unitSphere_innerProduct1 unitSphere_innerProduct1-class
An S4 class to represent the function prod_{i=1}^n x_i^{a_i} on S^{n-1}unitSphere_polynomial unitSphere_polynomial-class