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:Xiongtao Dai [aut, cre, cph], Zhenhua Lin [aut]

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'))

Peer review:

Uses libs:
  • openblas– Optimized BLAS
  • c++– GNU Standard C++ Library v3

This package does not link to any Github/Gitlab/R-forge repository. No issue tracker or development information is available.

openblascpp

1.48 score 1 stars 1 packages 4 scripts 166 downloads 30 exports 4 dependencies

Last updated 2 years agofrom:444c04e16d. Checks:OK: 1 NOTE: 1. Indexed: yes.

TargetResultDate
Doc / VignettesOKNov 25 2024
R-4.5-linux-x86_64NOTENov 25 2024

Exports:axisAngleRepbasisTancalcAmbDimcalcGeomParcalcIntDimcalcTanDimcoordToTanVcreateMdistanceExpMfrechetMeanfrechetMediangeodesicCurveGetSettingNameis.finiteDimlistAvailMfdLogMLogMSPDMakeSymmetricnormNormalizeoriginprojectprojectTangentrieExprieLogrmfdrunifSpheretanVToCoord

Dependencies:latticeMatrixRcppRcppArmadillo

Readme and manuals

Help Manual

Help pageTopics
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 spacebasisTan basisTan.Euclidean basisTan.FlatTorus basisTan.SO basisTan.SPD basisTan.Sphere
Transform the coordinates for the tangent space into a tangent vectorcoordToTanV coordToTanV.default
Create an object to symbolize the manifold.createM
Dimensions in this packagecalcAmbDim calcGeomPar calcIntDim calcTanDim dimensions
Geodesic distancedistance distance.AffInv distance.Dens distance.Euclidean distance.HS distance.L2 distance.LogEu distance.SO distance.Sphere
Matrix exponentialExpM
Calculate the Fréchet meanfrechetMean frechetMean.default
Calculate the Fréchet medianfrechetMedian frechetMedian.default
Obtain the geodesic curvegeodesicCurve geodesicCurve.HS geodesicCurve.Sphere
Helper function for simulationsGetSettingName
Tell whether a manifold is a finite-dimensional oneis.finiteDim
List all available manifold nameslistAvailMfd
Matrix logarithmLogM
Matrix logarithm of a symmetric positive definiteLogMSPD
Make a symmetric matrix by specifying a near-symmetric matrix M, or the lower triangular elements lowerTri with diagonal.MakeSym
manifold: Operations for Riemannian manifoldsmanifold
Returns the Riemannian metricmetric 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 metricnorm norm.AffInv norm.default norm.Dens norm.Euclidean norm.HS norm.L2 norm.LogEu norm.SO norm.Sphere
Normalize a vectorNormalize
Returns the origin of the manifoldorigin origin.Dens origin.Euclidean origin.HS origin.L2 origin.SO origin.SPD origin.Sphere
Project data points in the ambient space onto the manifoldproject 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 spaceprojectTangent projectTangent.Dens projectTangent.Euclidean projectTangent.HS projectTangent.L2 projectTangent.SO projectTangent.SPD projectTangent.Sphere
Riemannian exponential maprieExp rieExp.AffInv rieExp.Dens rieExp.Euclidean rieExp.HS rieExp.L2 rieExp.LogEu rieExp.SO rieExp.Sphere
Riemannian logarithm maprieLog rieLog.AffInv rieLog.Dens rieLog.Euclidean rieLog.HS rieLog.L2 rieLog.LogEu rieLog.SO rieLog.Sphere
Generate random variables on the manifoldrmfd rmfd.default
Generate uniform random variables on the unit sphererunifSphere
Transform tangent vectors to their coordinates on the tangent spacetanVToCoord tanVToCoord.default