hyperg_1F1_vec_b

hyperg_2F1_mat_a_vec_c

gsl_wrap

These are internal C++ functions which wrap hypergeometric
functions from GSL with vectorization. These are for
particular use cases in this package, and direct access by the user is
not assumed.

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. 

hyperg_1F1_vec_b function

<dl><dt>a, b</dt>
<dd>Parameters of hypergeometric functions; passed as <code>double</code></dd>
<dt>bvec, cvec</dt>
<dd>Parameters of hypergeometric functions; passed as
<code>Rcpp::NumericVector</code></dd>
<dt>x</dt>
<dd>Argument of hypergeometric functions; passed as <code>double</code></dd>
<dt>Amat</dt>
<dd>Parameter of hypergeometric functions; passed as
<code>Rcpp::NumericMatrix</code>. Dimension must be square of the length of
<code>cvec</code>.</dd></dl>

Arguments

<ul>
<li><code>hyperg_1F1_vec_b()</code>: wrapper of <code>gsl_hyperg_1F1_e()</code>, looping along <code>bvec</code></li>
<li><code>hyperg_2F1_mat_a_vec_c()</code>: wrapper of <code>gsl_hyperg_2F1_e()</code>, looping along <code>Amat</code> and
recycling <code>cvec</code></li>
</ul>

Functions

Internal C++ wrappers for GSL — hyperg_1F1_vec_b

<dl>

<dt>a, b</dt>
<dd>Parameters of hypergeometric functions; passed as <code>double</code></dd>


<dt>bvec, cvec</dt>
<dd>Parameters of hypergeometric functions; passed as
<code>Rcpp::NumericVector</code></dd>


<dt>x</dt>
<dd>Argument of hypergeometric functions; passed as <code>double</code></dd>


<dt>Amat</dt>
<dd>Parameter of hypergeometric functions; passed as
<code>Rcpp::NumericMatrix</code>. Dimension must be square of the length of
<code>cvec</code>.</dd>

</dl>

hyperg_1F1_vec_b: Internal C++ wrappers for GSL

Description

Usage

Value

Arguments

Functions