rmfd: Generate random variables on the manifold

In manifold: Operations for Riemannian Manifolds

Generate random variables on the manifold

Description

By default, random variables are generated by mapping isotropic Gaussian distributions on the tangent space back to the manifold using the exponential map

Usage

rmfd(mfd, n, dimIntrinsic, ...)

## Default S3 method:
rmfd(
  mfd,
  n,
  dimIntrinsic,
  p,
  dist = c("norm", "unif", "exp"),
  totalVar = 1,
  ...
)

Arguments

mfd	A manifold object created by createM
n	Sample size
dimIntrinsic	The intrinsic dimension of the target manifold
...	Passed into specific methods
p	Optionally, specify the base point of the tangent space, on which random tangent vectors will be generated. Default to the origin of 'mfd'.
dist	Either a string or a function, describing the distributions. If it is character, then independent univariate r.v. following that distribution with total variance 1 is generated on the tangent space. If it is a function, it should specify the generation of the samples on the tangent space _coordinates_ (with dimension dimIntrinsic), and it must return a matrix for which the columns are the coordinates. Then it will be mapped to the tangent space at the origin and then to the manifold.
totalVar	Total variance (sum of diagonal of the covariance matrix) of the tangent random vector

Value

A matrix with n columns, each containing a random sample on the manifold

Methods (by class)

• rmfd(default): Default method

manifold documentation built on Oct. 4, 2022, 5:06 p.m.