% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/HelperFunctions.R
\name{matsqrt}
\alias{matsqrt}
\title{Calculate Matrix Square Root for Symmetric Matrices}
\usage{
matsqrt(mat)
}
\arguments{
\item{mat}{A symmetric matrix \eqn{\textbf{M}}}
}
\value{
A matrix \eqn{\textbf{B}} such that \eqn{\textbf{B}\textbf{B}}
  equals \eqn{\textbf{M}} on the positive-eigenvalue subspace, with
  non-positive components truncated to 0.
}
\description{
Calculate Matrix Square Root for Symmetric Matrices
}
\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 \code{Vhalf_fxn}, or more
directly to build the \eqn{\mathbf{V}^{1/2}} input supplied to
\code{\link{lgspline}} for correlation-aware fits.
}
\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)

}
