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:
multIntTestFunc_0.3.0.tar.gz
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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)
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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')) |
Bug tracker:https://github.com/klausherrmann/multinttestfunc/issues
Last updated 8 days agofrom:14ec16c309. Checks:OK: 7. Indexed: yes.
| Target | Result | Date |
|---|---|---|
| Doc / Vignettes | OK | Sep 09 2024 |
| R-4.5-win | OK | Sep 09 2024 |
| R-4.5-linux | OK | Sep 09 2024 |
| R-4.4-win | OK | Sep 09 2024 |
| R-4.4-mac | OK | Sep 09 2024 |
| R-4.3-win | OK | Sep 09 2024 |
| R-4.3-mac | OK | Sep 09 2024 |
Exports:checkClosedUnitBallcheckClosedUnitCubecheckPoscheckRncheckStandardSimplexcheckUnitSpheredomainCheckdomainCheckPevaluateexactIntegralgetIntegrationDomaingetReferencesgetTagspIntRulePn_lognormalDensityPn_logtDensityRn_floorNormRn_GaussRn_normalDensityRn_tDensitystandardSimplex_DirichletstandardSimplex_exp_sumunitBall_normGaussunitBall_polynomialunitCube_BFN1unitCube_BFN2unitCube_BFN3unitCube_BFN4unitCube_cos2unitCube_floorunitCube_Genz1unitCube_maxunitSphere_innerProduct1unitSphere_polynomial
Integration Test for Rn
Rendered fromIntegration_Test_Rn.Rmdusingknitr::rmarkdownon Sep 09 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 Sep 09 2024.Last update: 2023-04-18
Started: 2021-10-04
Readme and manuals
Help Manual
| Help page | Topics |
|---|---|
| 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]^n | checkClosedUnitCube |
| Domain check for [0,Inf)^n | checkPos |
| Domain check for R^n | checkRn |
| 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 instance | domainCheck 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 points | evaluate 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 instance | exactIntegral 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 instance | getIntegrationDomain 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 instance | getReferences 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 instance | getTags 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 weights | pIntRule |
| 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 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)^n | Pn_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^n | Rn_floorNorm Rn_floorNorm-class |
| An S4 class to represent the function \exp(-\vec{x}\cdot\vec{x}) on R^n | Rn_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^n | Rn_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^n | Rn_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_n | standardSimplex_Dirichlet standardSimplex_Dirichlet-class |
| An S4 class to represent the function \exp(-c(x_1 + ... + x_n)) on T_n | standardSimplex_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_n | unitBall_polynomial unitBall_polynomial-class |
| An S4 class to represent the function prod^{n}_{i=1}\vert 4x_i-2\vert on [0,1]^n | unitCube_BFN1 unitCube_BFN1-class |
| An S4 class to represent the function prod^{n}_{i=1} i\cos(ix_i) on [0,1]^n | unitCube_BFN2 unitCube_BFN2-class |
| An S4 class to represent the function prod^{n}_{i=1} T_{nu(i)}(2x_i-1) on [0,1]^n | unitCube_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]^n | unitCube_BFN4 unitCube_BFN4-class |
| An S4 class to represent the function (\cos(\vec{x}\cdot\vec{v}))^2 on [0,1]^n | unitCube_cos2 unitCube_cos2-class |
| An S4 class to represent the function \lfloor x_1 + ... + x_n \rfloor on [0,1]^n | unitCube_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]^n | unitCube_Genz1 unitCube_Genz1-class |
| An S4 class to represent the function \max(x_1,...,x_n) on [0,1]^n | unitCube_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 |