prinang: Calculate Principal Angles Between Subspaces

In bbuchsbaum/multivarious: Extensible Data Structures for Multivariate Analysis

Calculate Principal Angles Between Subspaces

Description

Computes the principal angles between two subspaces defined by the columns of two orthonormal matrices Q1 and Q2.

Usage

prinang(Q1, Q2)

Arguments

Q1	An n x p matrix whose columns form an orthonormal basis for the first subspace.
Q2	An n x q matrix whose columns form an orthonormal basis for the second subspace.

Value

A numeric vector containing the principal angles in radians, sorted in ascending order. The number of angles is min(p, q).

Examples

# Example: Angle between xy-plane and a plane rotated 45 degrees around x-axis
Q1 <- cbind(c(1,0,0), c(0,1,0)) # xy-plane basis
theta <- pi/4
R <- matrix(c(1, 0, 0, 0, cos(theta), sin(theta), 0, -sin(theta), cos(theta)), 3, 3)
Q2 <- R %*% Q1 # Rotated basis
angles_rad <- prinang(Q1, Q2)
angles_deg <- angles_rad * 180 / pi
print(angles_deg) # Should be approximately 0 and 45 degrees

# Example with PCA loadings (after ensuring orthonormality if needed)
# Assuming pca1$v and pca2$v are loading matrices (variables x components)
# Orthonormalize them first if they are not already (e.g., from standard SVD)
# Q1 <- qr.Q(qr(pca1$v[, 1:3]))
# Q2 <- qr.Q(qr(pca2$v[, 1:3]))
# prinang(Q1, Q2)

bbuchsbaum/multivarious documentation built on July 16, 2025, 11:04 p.m.