runif_sm {SMFilter}

Sample from the uniform distribution on the Stiefel manifold.

Description

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

Usage

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 \geq 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, [e-mail]

Examples

runif_sm(10,4,2)