matsqrt: Calculate Matrix Square Root for Symmetric Matrices

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Calculate Matrix Square Root for Symmetric Matrices

Description

Calculate Matrix Square Root for Symmetric Matrices

Usage

matsqrt(mat)

Arguments

mat	A symmetric matrix \textbf{M}

Details

Uses an eigenvalue-decomposition-based approach.

Non-positive eigenvalues are set to 0 before taking fourth roots.

This implementation is particularly useful for whitening procedures in GLMs with correlation structures and for computing variance-covariance matrices under constraints.

You can use this to help construct a custom Vhalf_fxn, or more directly to build the \mathbf{V}^{1/2} input supplied to lgspline for correlation-aware fits.

Value

A matrix \textbf{B} such that \textbf{B}\textbf{B} equals \textbf{M} on the positive-eigenvalue subspace, with non-positive components truncated to 0.

Examples

## Identity matrix
m1 <- diag(2)
matsqrt(m1)  # Returns identity matrix

## Compound symmetry correlation matrix
rho <- 0.5
m2 <- matrix(rho, 3, 3) + diag(1-rho, 3)
B <- matsqrt(m2)
# Verify: B %**% B approximately equals m2
all.equal(B %**% B, m2)

## Example for correlation structure
n_blocks <- 2  # Number of subjects
block_size <- 3  # Measurements per subject
rho <- 0.7  # Within-subject correlation
# Correlation matrix for one subject
R <- matrix(rho, block_size, block_size) +
     diag(1-rho, block_size)
# Full correlation matrix for all subjects
V <- kronecker(diag(n_blocks), R)
Vhalf <- matsqrt(V)

lgspline documentation built on May 8, 2026, 5:07 p.m.