Random Orthonormal Matrix Generation and Optimization on the Stiefel Manifold

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Documentation for package ‘rstiefel’ version 1.0.1

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

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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