# Operations for Riemannian Manifolds

## Documentation for package ‘manifold’ version 0.1.1

- DESCRIPTION file.

## Help Pages

A B C D E F G I L M N O P R T

## -- A --

axisAngleRep | Returns the angle representation of SO(3) matrices c.f. <URL: https://en.wikipedia.org/wiki/Axis-angle_representation>

## -- B --

basisTan | Obtain an orthonormal basis on the tangent space
basisTan.Euclidean | Obtain an orthonormal basis on the tangent space
basisTan.FlatTorus | Obtain an orthonormal basis on the tangent space
basisTan.SO | Obtain an orthonormal basis on the tangent space
basisTan.SPD | Obtain an orthonormal basis on the tangent space
basisTan.Sphere | Obtain an orthonormal basis on the tangent space

## -- C --

calcAmbDim | Dimensions in this package
calcGeomPar | Dimensions in this package
calcIntDim | Dimensions in this package
calcTanDim | Dimensions in this package
coordToTanV | Transform the coordinates for the tangent space into a tangent vector
coordToTanV.default | Transform the coordinates for the tangent space into a tangent vector
createM | Create an object to symbolize the manifold.

## -- D --

dimensions | Dimensions in this package
distance | Geodesic distance
distance.AffInv | Geodesic distance
distance.Dens | Geodesic distance
distance.Euclidean | Geodesic distance
distance.HS | Geodesic distance
distance.L2 | Geodesic distance
distance.LogEu | Geodesic distance
distance.SO | Geodesic distance
distance.Sphere | Geodesic distance

## -- E --

ExpM | Matrix exponential

## -- F --

frechetMean | Calculate the Fréchet mean
frechetMean.default | Calculate the Fréchet mean
frechetMedian | Calculate the Fréchet median
frechetMedian.default | Calculate the Fréchet median

## -- G --

geodesicCurve | Obtain the geodesic curve
geodesicCurve.HS | Obtain the geodesic curve
geodesicCurve.Sphere | Obtain the geodesic curve
GetSettingName | Helper function for simulations

## -- I --

is.finiteDim | Tell whether a manifold is a finite-dimensional one

## -- L --

listAvailMfd | List all available manifold names
LogM | Matrix logarithm
LogMSPD | Matrix logarithm of a symmetric positive definite

## -- M --

MakeSym | Make a symmetric matrix by specifying a near-symmetric matrix M, or the lower triangular elements lowerTri with diagonal.
manifold | manifold: Operations for Riemannian manifolds
metric | Returns the Riemannian metric
metric.AffInv | Returns the Riemannian metric
metric.default | Returns the Riemannian metric
metric.Dens | Returns the Riemannian metric
metric.Euclidean | Returns the Riemannian metric
metric.HS | Returns the Riemannian metric
metric.LogEu | Returns the Riemannian metric
metric.SO | Returns the Riemannian metric
metric.Sphere | Returns the Riemannian metric

## -- N --

norm | Norm on the tangent space induced by the Riemannian metric
norm.AffInv | Norm on the tangent space induced by the Riemannian metric
norm.default | Norm on the tangent space induced by the Riemannian metric
norm.Dens | Norm on the tangent space induced by the Riemannian metric
norm.Euclidean | Norm on the tangent space induced by the Riemannian metric
norm.HS | Norm on the tangent space induced by the Riemannian metric
norm.L2 | Norm on the tangent space induced by the Riemannian metric
norm.LogEu | Norm on the tangent space induced by the Riemannian metric
norm.SO | Norm on the tangent space induced by the Riemannian metric
norm.Sphere | Norm on the tangent space induced by the Riemannian metric
Normalize | Normalize a vector

## -- O --

origin | Returns the origin of the manifold
origin.Dens | Returns the origin of the manifold
origin.Euclidean | Returns the origin of the manifold
origin.HS | Returns the origin of the manifold
origin.L2 | Returns the origin of the manifold
origin.SO | Returns the origin of the manifold
origin.SPD | Returns the origin of the manifold
origin.Sphere | Returns the origin of the manifold

## -- P --

project | Project data points in the ambient space onto the manifold
project.AffInv | Project data points in the ambient space onto the manifold
project.Dens | Project data points in the ambient space onto the manifold
project.Euclidean | Project data points in the ambient space onto the manifold
project.HS | Project data points in the ambient space onto the manifold
project.L2 | Project data points in the ambient space onto the manifold
project.LogEu | Project data points in the ambient space onto the manifold
project.SO | Project data points in the ambient space onto the manifold
project.SPD | Project data points in the ambient space onto the manifold
project.Sphere | Project data points in the ambient space onto the manifold
projectTangent | Project data points in the ambient space onto the tangent space
projectTangent.Dens | Project data points in the ambient space onto the tangent space
projectTangent.Euclidean | Project data points in the ambient space onto the tangent space
projectTangent.HS | Project data points in the ambient space onto the tangent space
projectTangent.L2 | Project data points in the ambient space onto the tangent space
projectTangent.SO | Project data points in the ambient space onto the tangent space
projectTangent.SPD | Project data points in the ambient space onto the tangent space
projectTangent.Sphere | Project data points in the ambient space onto the tangent space

## -- R --

rieExp | Riemannian exponential map
rieExp.AffInv | Riemannian exponential map
rieExp.Dens | Riemannian exponential map
rieExp.Euclidean | Riemannian exponential map
rieExp.HS | Riemannian exponential map
rieExp.L2 | Riemannian exponential map
rieExp.LogEu | Riemannian exponential map
rieExp.SO | Riemannian exponential map
rieExp.Sphere | Riemannian exponential map
rieLog | Riemannian logarithm map
rieLog.AffInv | Riemannian logarithm map
rieLog.Dens | Riemannian logarithm map
rieLog.Euclidean | Riemannian logarithm map
rieLog.HS | Riemannian logarithm map
rieLog.L2 | Riemannian logarithm map
rieLog.LogEu | Riemannian logarithm map
rieLog.SO | Riemannian logarithm map
rieLog.Sphere | Riemannian logarithm map
rmfd | Generate random variables on the manifold
rmfd.default | Generate random variables on the manifold
runifSphere | Generate uniform random variables on the unit sphere

## -- T --

tanVToCoord | Transform tangent vectors to their coordinates on the tangent space
tanVToCoord.default | Transform tangent vectors to their coordinates on the tangent space