sum_counterdiag

sum_counterdiag3D

<code>sum_counterdiag()</code> sums up counter-diagonal elements of
a square matrix from the upper-left; i.e.,
<code>c(X[1, 1], X[1, 2] + X[2, 1], X[1, 3] + X[2, 2] + X[3, 1], ...)</code>
(or a sequence of \(\sum_{i=1}^k x_{i, k - i + 1}\) for
\(k = 1, 2, ...\)). <code>sum_counterdiag3D()</code> does a comparable in
a 3D cubic array. No check is done on the structure of <code>X</code>.

Evaluates moments of ratios (and products) of quadratic forms
in normal variables, specifically using recursive algorithms developed by
Bao and Kan (2013) <doi:10.1016/j.jmva.2013.03.002> and Hillier et al.
(2014) <doi:10.1017/S0266466613000364>. Also provides distribution,
quantile, and probability density functions of simple ratios of quadratic
forms in normal variables with several algorithms. Originally developed as
a supplement to Watanabe (2023) <doi:10.1007/s00285-023-01930-8> for
evaluating average evolvability measures in evolutionary quantitative
genetics, but can be used for a broader class of statistics. Generating
functions for these moments are also closely related to the top-order zonal
and invariant polynomials of matrix arguments.

Junya Watanabe

qfratio

Moments and Distributions of Ratios of Quadratic Forms Using
Recursion

Patrick Alken

Brian Gough

Pavel Holoborodko

Gerard Jungman

Reid Priedhorsky

Free Software Foundation, Inc. 

sum_counterdiag function

<dl><dt>X</dt>
<dd>Square matrix or cubic array</dd></dl>

Arguments

Summing up counter-diagonal elements — sum_counterdiag

<dl>

<dt>X</dt>
<dd>Square matrix or cubic array</dd>

</dl>

sum_counterdiag: Summing up counter-diagonal elements

Description

Usage

Arguments