Tests for Geophysical Eigenvalues
Bootstrap calibration for single-sample and k-sample tests
Chi Squared Calibration for Testing
Eigenvalue confidence region under fixed trace constraint
Eigenvalue confidence interval under trace=0 and sum of square constra...
Compute the Covariance of Eigenvalues
Estimate parameters of orthogonally invariant covariance
Flat storage of symmetric matrices
Check if the supplied sample(s) have fixed trace
Check whether the supplied sample(s) have equal sum of squared eigenva...
Normalise so that Sum of Squared Eigenvalues is One
Scale symmetric matrices to have trace of one
Project diagonal elements to have trace of zero
Simulate Symmetric Matrices with Multivariate Normal Elements
Simulate Symmetric Matrices with Multivariate t Elements
Test for eigenvalues when trace is fixed
Test of eigenvalue multiplicity assuming orthogonally invariant covari...
Test eigenvalue multiplicity
Test for eigenvalues when sum of squared eigenvalues is 1
Test eigenvalues when trace=0 and sum of square eigenvalues = 1
Two Sample Test of Equal Eigenvalues Using GOE Approximation
Pivotal bootstrap test of mean eigenvalues
TFORGE: Tests for Geophysical Eigenvalues
Flatten a symmetric matrix into a vector preserving Frobenius norm.
Flatten a symmetric matrix into a vector.
The eigenvalues of observed symmetric matrices are often of intense scientific interest. This package offers single sample tests for the eigenvalues of the population mean or the eigenvalue-multiplicity of the population mean. For k-samples, this package offers tests for equal eigenvalues between samples. Included is support for matrices with constraints common to geophysical tensors (constant trace, sum of squared eigenvalues, or both) and eigenvectors are usually considered nuisance parameters. Pivotal bootstrap methods enable these tests to have good performance for small samples (n=15 for 3x3 matrices). These methods were developed and studied by Hingee, Scealy and Wood (2026, "Nonparametric bootstrap inference for the eigenvalues of geophysical tensors", accepted by the Journal of American Statistical Association). Also available is a 2-sample test using a Gaussian orthogonal ensemble approximation and an eigenvalue-multiplicity test that assumes orthogonally-invariant covariance.