# runif_sm: Sample from the uniform distribution on the Stiefel manifold. In SMFilter: Filtering Algorithms for the State Space Models on the Stiefel Manifold

## Description

This function draws a sample from the uniform distribution on the Stiefel manifold.

## Usage

 1 runif_sm(num, ip, ir) 

## Arguments

 num number of observations or sample size. ip the first dimension p of the matrix. ir the second dimension r of the matrix.

## Details

The Stiefel manifold with dimension p and r (p ≥q r) is a space whose points are r-frames in R^p. A set of r orthonormal vectors in R^p is called an r-frame in R^p. The Stiefel manifold is a collection of p \times r full rank matrices X such that X'X = I_r.

## Value

an array with dimension num, ip and ir containing a sample of draws from the uniform distribution on the Stiefel manifold.

## Author(s)

Yukai Yang, yukai.yang@statistik.uu.se

## Examples

 1 runif_sm(10,4,2) 

SMFilter documentation built on May 1, 2019, 8:01 p.m.