Package: TFORGE 0.1.17

TFORGE: Tests for Geophysical Eigenvalues

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, <doi:10.1080/01621459.2025.2606381>). Also available is a 2-sample test using a Gaussian orthogonal ensemble approximation and an eigenvalue-multiplicity test that assumes orthogonally-invariant covariance.

Authors:Kassel Liam Hingee [aut, cre], Art B. Owen [cph], Board of Trustees Leland Stanford Junior University [cph]

TFORGE_0.1.17.tar.gz
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manual.pdf |manual.html✨
DESCRIPTION |NEWS
card.svg |card.png
TFORGE/json (API)

# Install 'TFORGE' in R:

install.packages('TFORGE', repos = c('https://kasselhingee.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/kasselhingee/tforge/issues

Datasets:

Gonjo - AMS data of the Gonjo Basin

On CRAN:

4.48 score 2 scripts 347 downloads 39 exports 10 dependencies

Last updated from:1dcf48670d. Checks:1 ERROR, 8 OK. Indexed: yes.

Target	Result	Time
linux-devel-x86_64	ERROR	142
source / vignettes	OK	194
linux-release-x86_64	OK	145
macos-release-arm64	OK	97
macos-oldrel-arm64	OK	102
windows-devel	OK	96
windows-release	OK	106
windows-oldrel	OK	92
wasm-release	OK	105

Exports:as_flat as_fsm as_kfsm boot_calib chisq_calib conf_fixedtrace conf_fixedtrace_inregion conf_ss1fixedtrace conf_ss1fixedtrace_inregion cov_evals dim_vech estimate_OIcov has_fixedtrace has_ss1 inv_vech normalise_ss1 normalise_trace normalize_trace project_trace rsymm rsymm_norm rsymm_t stat_fixedtrace stat_multiplicity stat_ss1 stat_ss1fixedtrace stat_unconstrained test_fixedtrace test_multiplicity test_multiplicity_nonnegative test_multiplicity_OI test_ss1 test_ss1fixedtrace test_unconstrained test_unconstrained_aGOE translate_evalsofav translate2multiplicity vecd vech

Dependencies:cli glue lifecycle magrittr mvtnorm purrr rbibutils Rdpack rlang vctrs

Gonjo Demonstration

Preparation | Multiplicity Tests | 3-Sample Test | Confidence Regions | References

Rendered fromGonjo_demo.Rmdusingknitr::rmarkdown

Last update: 2025-12-13
Started: 2025-12-12

Help page	Topics
TFORGE: Tests for Geophysical Eigenvalues	TFORGE-package TFORGE
Bootstrap calibration for single-sample and k-sample tests	boot_calib
Chi Squared Calibration for Testing	chisq_calib
Eigenvalue confidence region under fixed trace constraint	conf_fixedtrace conf_fixedtrace_inregion
Eigenvalue confidence interval under trace=0 and sum of square constraint	conf_ss1fixedtrace conf_ss1fixedtrace_inregion
Compute the Covariance of Eigenvalues	cov_evals
Estimate parameters of orthogonally invariant covariance	estimate_OIcov
Flat storage of symmetric matrices	as_flat as_fsm as_kfsm fsm kfsm
AMS data of the Gonjo Basin	Gonjo
Check if the supplied sample(s) have fixed trace	has_fixedtrace
Check whether the supplied sample(s) have equal sum of squared eigenvalues	has_ss1
Normalise so that Sum of Squared Eigenvalues is One	normalise_ss1
Scale symmetric matrices to have trace of one	normalise_trace normalize_trace
Project diagonal elements to have trace of zero	project_trace
Simulate Symmetric Matrices with Multivariate Normal Elements	rsymm rsymm_norm
Simulate Symmetric Matrices with Multivariate t Elements	rsymm_t
Test for eigenvalues when trace is fixed	stat_fixedtrace test_fixedtrace
Test eigenvalue multiplicity	stat_multiplicity test_multiplicity test_multiplicity_nonnegative translate2multiplicity
Test of eigenvalue multiplicity assuming orthogonally invariant covariance	test_multiplicity_OI
Test for eigenvalues when sum of squared eigenvalues is 1	stat_ss1 test_ss1
Test eigenvalues when trace=0 and sum of square eigenvalues = 1	stat_ss1fixedtrace test_ss1fixedtrace
Pivotal bootstrap test of mean eigenvalues	stat_unconstrained test_unconstrained translate_evalsofav
Two Sample Test of Equal Eigenvalues Using GOE Approximation	test_unconstrained_aGOE
Flatten a symmetric matrix into a vector preserving Frobenius norm.	vecd
Flatten a symmetric matrix into a vector.	dim_vech inv_vech vech

Package: TFORGE 0.1.17

TFORGE: Tests for Geophysical Eigenvalues

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