is_diagonal

This internal function is used to determine whether a square matrix
is diagonal (within a specified tolerance). Returns <code>TRUE</code>
when the absolute values of all off-diagonal elements
are below <code>tol</code>, using <code><a href="/link/all.equal()?package=qfratio&version=1.1.1" data-mini-rdoc="qfratio::all.equal()">all.equal()</a></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. 

is_diagonal function

<dl><dt>A</dt>
<dd>Square matrix. No check is done.</dd>
<dt>tol</dt>
<dd>Numeric to specify <code>tolerance</code> in <code><a href="/link/all.equal()?package=qfratio&version=1.1.1" data-mini-rdoc="qfratio::all.equal()">all.equal()</a></code></dd>
<dt>symmetric</dt>
<dd>If <code>FALSE</code> (default), sum of absolute values of the corresponding
lower and upper triangular elements are examined with a doubled
<code>tol</code>. If <code>TRUE</code>, only the lower triangular elements are
examined assuming symmetry.</dd></dl>

Arguments

This internal function is used to determine whether a square matrix
is diagonal (within a specified tolerance). Returns <code>TRUE</code>
when the absolute values of all off-diagonal elements
are below <code>tol</code>, using <code><a href='https://rdrr.io/r/base/all.equal.html'>all.equal()</a></code>.

Is this matrix diagonal? — is_diagonal

<dl>

<dt>A</dt>
<dd>Square matrix. No check is done.</dd>


<dt>tol</dt>
<dd>Numeric to specify <code>tolerance</code> in <code><a href='https://rdrr.io/r/base/all.equal.html'>all.equal()</a></code></dd>


<dt>symmetric</dt>
<dd>If <code>FALSE</code> (default), sum of absolute values of the corresponding
lower and upper triangular elements are examined with a doubled
<code>tol</code>. If <code>TRUE</code>, only the lower triangular elements are
examined assuming symmetry.</dd>

</dl>

is_diagonal: Is this matrix diagonal?

Description

Usage

Arguments

See Also