R: Random Orthonormal Matrix Generation and Optimization on the Stiefel Manifold

# Random Orthonormal Matrix Generation and Optimization on the Stiefel Manifold

## Documentation for package ‘rstiefel’ version 1.0.1

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

rstiefel-package | Random Orthonormal Matrix Generation on the Stiefel Manifold #' Simulation of random orthonormal matrices from linear and quadratic exponential family distributions on the Stiefel manifold. The most general type of distribution covered is the matrix-variate Bingham-von Mises-Fisher distribution. Most of the simulation methods are presented in Hoff(2009) "Simulation of the Matrix Bingham-von Mises-Fisher Distribution, With Applications to Multivariate and Relational Data" <doi:10.1198/jcgs.2009.07177>. The package also includes functions for optimzation on the Stiefel manifold based on algoirthms described in Wen and Yin (2013) "A feasible method for optimization with orthogonality constraints" <doi:10.1007/s10107-012-0584-1>.
lineSearch | A curvilinear search on the Stiefel manifold (Wen and Yin 2013, Algo 1)
lineSearchBB | A curvilinear search on the Stiefel manifold with BB steps (Wen and Yin 2013, Algo 2) This is based on the line search algorithm described in (Zhang and Hager, 2004)
NullC | Null Space of a Matrix
optStiefel | Optimize a function on the Stiefel manifold
rbing.matrix.gibbs | Gibbs Sampling for the Matrix-variate Bingham Distribution
rbing.O2 | Simulate a 2*2 Orthogonal Random Matrix
rbing.Op | Simulate a 'p*p' Orthogonal Random Matrix
rbing.vector.gibbs | Gibbs Sampling for the Vector-variate Bingham Distribution
rbmf.matrix.gibbs | Gibbs Sampling for the Matrix-variate Bingham-von Mises-Fisher Distribution.
rbmf.O2 | Simulate a '2*2' Orthogonal Random Matrix
rbmf.vector.gibbs | Gibbs Sampling for the Vector-variate Bingham-von Mises-Fisher Distribution
rmf.matrix | Simulate a Random Orthonormal Matrix
rmf.matrix.gibbs | Gibbs Sampling for the Matrix-variate von Mises-Fisher Distribution
rmf.vector | Simulate a Random Normal Vector
rstiefel | Random Orthonormal Matrix Generation on the Stiefel Manifold #' Simulation of random orthonormal matrices from linear and quadratic exponential family distributions on the Stiefel manifold. The most general type of distribution covered is the matrix-variate Bingham-von Mises-Fisher distribution. Most of the simulation methods are presented in Hoff(2009) "Simulation of the Matrix Bingham-von Mises-Fisher Distribution, With Applications to Multivariate and Relational Data" <doi:10.1198/jcgs.2009.07177>. The package also includes functions for optimzation on the Stiefel manifold based on algoirthms described in Wen and Yin (2013) "A feasible method for optimization with orthogonality constraints" <doi:10.1007/s10107-012-0584-1>.
rustiefel | Siumlate a Uniformly Distributed Random Orthonormal Matrix
rW | Simulate 'W' as Described in Wood(1994)
ry_bing | Helper Function for Sampling a Bingham-distributed Vector
ry_bmf | Helper Function for Sampling a Bingham-von Mises-Fisher-distributed Vector
tr | Compute the trace of a matrix