Operations for Riemannian Manifolds

Documentation for package ‘manifold’ version 0.1.1

Help Pages

-- A --

Returns the angle representation of SO(3) matrices c.f. <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 --

-- 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 --

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