Package: manifold 0.1.1
Xiongtao Dai
manifold: Operations for Riemannian Manifolds
Implements operations for Riemannian manifolds, e.g., geodesic distance, Riemannian metric, exponential and logarithm maps, etc. Also incorporates random object generator on the manifolds. See Dai, Lin, and Müller (2021) <doi:10.1111/biom.13385>.
Authors:
manifold_0.1.1.tar.gz
manifold_0.1.1.tar.gz(r-4.5-noble)manifold_0.1.1.tar.gz(r-4.4-noble)
manifold_0.1.1.tgz(r-4.4-emscripten)manifold_0.1.1.tgz(r-4.3-emscripten)
manifold.pdf |manifold.html✨
manifold/json (API)
| # Install 'manifold' in R: |
| install.packages('manifold', repos = c('https://cran.r-universe.dev', 'https://cloud.r-project.org')) |
This package does not link to any Github/Gitlab/R-forge repository. No issue tracker or development information is available.
Last updated 2 years agofrom:444c04e16d. Checks:OK: 1 NOTE: 1. Indexed: yes.
| Target | Result | Date |
|---|---|---|
| Doc / Vignettes | OK | Aug 27 2024 |
| R-4.5-linux-x86_64 | NOTE | Aug 27 2024 |
Exports:axisAngleRepbasisTancalcAmbDimcalcGeomParcalcIntDimcalcTanDimcoordToTanVcreateMdistanceExpMfrechetMeanfrechetMediangeodesicCurveGetSettingNameis.finiteDimlistAvailMfdLogMLogMSPDMakeSymmetricnormNormalizeoriginprojectprojectTangentrieExprieLogrmfdrunifSpheretanVToCoord
Dependencies:latticeMatrixRcppRcppArmadillo
Readme and manuals
Help Manual
| Help page | Topics |
|---|---|
| Returns the angle representation of SO(3) matrices c.f. <https://en.wikipedia.org/wiki/Axis-angle_representation> | axisAngleRep |
| Obtain an orthonormal basis on the tangent space | basisTan basisTan.Euclidean basisTan.FlatTorus basisTan.SO basisTan.SPD basisTan.Sphere |
| Transform the coordinates for the tangent space into a tangent vector | coordToTanV coordToTanV.default |
| Create an object to symbolize the manifold. | createM |
| Dimensions in this package | calcAmbDim calcGeomPar calcIntDim calcTanDim dimensions |
| Geodesic distance | distance distance.AffInv distance.Dens distance.Euclidean distance.HS distance.L2 distance.LogEu distance.SO distance.Sphere |
| Matrix exponential | ExpM |
| Calculate the Fréchet mean | frechetMean frechetMean.default |
| Calculate the Fréchet median | frechetMedian frechetMedian.default |
| Obtain the geodesic curve | geodesicCurve geodesicCurve.HS geodesicCurve.Sphere |
| Helper function for simulations | GetSettingName |
| Tell whether a manifold is a finite-dimensional one | is.finiteDim |
| List all available manifold names | listAvailMfd |
| Matrix logarithm | LogM |
| Matrix logarithm of a symmetric positive definite | LogMSPD |
| Make a symmetric matrix by specifying a near-symmetric matrix M, or the lower triangular elements lowerTri with diagonal. | MakeSym |
| manifold: Operations for Riemannian manifolds | manifold |
| Returns the Riemannian metric | metric metric.AffInv metric.default metric.Dens metric.Euclidean metric.HS metric.LogEu metric.SO metric.Sphere |
| Norm on the tangent space induced by the Riemannian metric | norm norm.AffInv norm.default norm.Dens norm.Euclidean norm.HS norm.L2 norm.LogEu norm.SO norm.Sphere |
| Normalize a vector | Normalize |
| Returns the origin of the manifold | origin origin.Dens origin.Euclidean origin.HS origin.L2 origin.SO origin.SPD origin.Sphere |
| Project data points in the ambient space onto the manifold | project project.AffInv project.Dens project.Euclidean project.HS project.L2 project.LogEu project.SO project.SPD project.Sphere |
| Project data points in the ambient space onto the tangent space | projectTangent projectTangent.Dens projectTangent.Euclidean projectTangent.HS projectTangent.L2 projectTangent.SO projectTangent.SPD projectTangent.Sphere |
| Riemannian exponential map | rieExp rieExp.AffInv rieExp.Dens rieExp.Euclidean rieExp.HS rieExp.L2 rieExp.LogEu rieExp.SO rieExp.Sphere |
| Riemannian logarithm map | rieLog rieLog.AffInv rieLog.Dens rieLog.Euclidean rieLog.HS rieLog.L2 rieLog.LogEu rieLog.SO rieLog.Sphere |
| Generate random variables on the manifold | rmfd rmfd.default |
| Generate uniform random variables on the unit sphere | runifSphere |
| Transform tangent vectors to their coordinates on the tangent space | tanVToCoord tanVToCoord.default |