prangles: Compute Principal Angles between subspaces

In JimSkinner/prangles: Provides function for computing Principal Angles

Description

This function takes two matrices, A and B, each defining a subspace via a set of basis vectors in columns. The Principal Angles between these subspaces are then computed and returned in radians. These matrices do not need to have the same number of rows, but must have the same number of columns; i.e., the subspaces defined must live in the same vector space, but do not need to share dimensionality. Vectors may be provided, and these are converted into single column matrices.

Usage

prangles(A, B)

Arguments

A	(d x n1) matrix containin basis for subspace A.
B	(d x n2) matrix containin basis for subspace B.

Value

A vector of min(n1, n2) principal angles in descending order (units in radians).

Examples

A <- matrix(c(1, 0, 0,
              0, 1, 0), nrow=3, ncol=2)
B <- matrix(c(1, 0, 0), nrow=3, ncol=1)
C <- matrix(c(0, 0, 1), nrow=3, ncol=1)
D <- matrix(c(B, C), nrow=3, ncol=2)

# Subspace B intersects with A, so gives the single PA of 0
anglesAB <- prangles(A, B)
stopifnot(anglesAB == 0)

# Subspace C is orthogonal to A, so has a PA of pi/2
anglesAC <- prangles(A, C)
stopifnot(all.equal(anglesAC, pi/2))

# A and D have PAs {pi/2, 0}, so they intersect along 1 dimension
anglesAD <- prangles(A, D)
stopifnot(all.equal(anglesAD, c(pi/2, 0)))

JimSkinner/prangles documentation built on May 28, 2019, 12:44 p.m.