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- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="math_toolkit.issues"></a><a class="link" href="issues.html" title="Known Issues, and TODO List">Known Issues, and TODO List</a>
- </h2></div></div></div>
- <p>
- Predominantly this is a TODO list, or a list of possible future enhancements.
- Items labled "High Priority" effect the proper functioning of the
- component, and should be fixed as soon as possible. Items labled "Medium
- Priority" are desirable enhancements, often pertaining to the performance
- of the component, but do not effect it's accuracy or functionality. Items labled
- "Low Priority" should probably be investigated at some point. Such
- classifications are obviously highly subjective.
- </p>
- <p>
- If you don't see a component listed here, then we don't have any known issues
- with it.
- </p>
- <h5>
- <a name="math_toolkit.issues.h0"></a>
- <span class="phrase"><a name="math_toolkit.issues.tgamma"></a></span><a class="link" href="issues.html#math_toolkit.issues.tgamma">tgamma</a>
- </h5>
- <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
- Can the <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
- be optimized any further? (low priority)
- </li></ul></div>
- <h5>
- <a name="math_toolkit.issues.h1"></a>
- <span class="phrase"><a name="math_toolkit.issues.incomplete_beta"></a></span><a class="link" href="issues.html#math_toolkit.issues.incomplete_beta">Incomplete
- Beta</a>
- </h5>
- <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
- Investigate Didonato and Morris' asymptotic expansion for large a and b
- (medium priority).
- </li></ul></div>
- <h5>
- <a name="math_toolkit.issues.h2"></a>
- <span class="phrase"><a name="math_toolkit.issues.inverse_gamma"></a></span><a class="link" href="issues.html#math_toolkit.issues.inverse_gamma">Inverse
- Gamma</a>
- </h5>
- <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
- Investigate whether we can skip iteration altogether if the first approximation
- is good enough (Medium Priority).
- </li></ul></div>
- <h5>
- <a name="math_toolkit.issues.h3"></a>
- <span class="phrase"><a name="math_toolkit.issues.polynomials"></a></span><a class="link" href="issues.html#math_toolkit.issues.polynomials">Polynomials</a>
- </h5>
- <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
- The Legendre and Laguerre Polynomials have surprisingly different error
- rates on different platforms, considering they are evaluated with only
- basic arithmetic operations. Maybe this is telling us something, or maybe
- not (Low Priority).
- </li></ul></div>
- <h5>
- <a name="math_toolkit.issues.h4"></a>
- <span class="phrase"><a name="math_toolkit.issues.elliptic_integrals"></a></span><a class="link" href="issues.html#math_toolkit.issues.elliptic_integrals">Elliptic
- Integrals</a>
- </h5>
- <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
- <li class="listitem">
- [para Carlson's algorithms (mainly R<sub>J</sub>) are somewhat prone to internal overflow/underflow
- when the arguments are very large or small. The homogeneity relations:]
- [para R<sub>F</sub>(ka, kb, kc) = k<sup>-1/2</sup> R<sub>F</sub>(a, b, c)] [para and] [para R<sub>J</sub>(ka, kb, kc,
- kr) = k<sup>-3/2</sup> R<sub>J</sub>(a, b, c, r)] [para could be used to sidestep trouble here:
- provided the problem domains can be accurately identified. (Medium Priority).]
- </li>
- <li class="listitem">
- There are a several other integrals: Bulirsch's <span class="emphasis"><em>el</em></span>
- functions that could be implemented using Carlson's integrals (Low Priority).
- </li>
- <li class="listitem">
- The integrals K(k) and E(k) could be implemented using rational approximations
- (both for efficiency and accuracy), assuming we can find them. (Medium
- Priority).
- </li>
- </ul></div>
- <h5>
- <a name="math_toolkit.issues.h5"></a>
- <span class="phrase"><a name="math_toolkit.issues.owen_s_t_function"></a></span><a class="link" href="issues.html#math_toolkit.issues.owen_s_t_function">Owen's
- T Function</a>
- </h5>
- <p>
- There is a problem area at arbitrary precision when <span class="emphasis"><em>a</em></span>
- is very close to 1. However, note that the value for <span class="emphasis"><em>T(h, 1)</em></span>
- is well known and easy to compute, and if we replaced the <span class="emphasis"><em>a<sup>k</sup></em></span>
- terms in series T1, T2 or T4 by <span class="emphasis"><em>(a<sup>k</sup> - 1)</em></span> then we would
- have the difference between <span class="emphasis"><em>T(h, a)</em></span> and <span class="emphasis"><em>T(h,
- 1)</em></span>. Unfortunately this doesn't improve the convergence of those
- series in that area. It certainly looks as though a new series in terms of
- <span class="emphasis"><em>(1-a)<sup>k</sup></em></span> is both possible and desirable in this area, but
- it remains elusive at present.
- </p>
- <h5>
- <a name="math_toolkit.issues.h6"></a>
- <span class="phrase"><a name="math_toolkit.issues.statistical_distributions"></a></span><a class="link" href="issues.html#math_toolkit.issues.statistical_distributions">Statistical
- distributions</a>
- </h5>
- <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
- Student's t Perhaps switch to normal distribution as a better approximation
- for very large degrees of freedom?
- </li></ul></div>
- <h5>
- <a name="math_toolkit.issues.h7"></a>
- <span class="phrase"><a name="math_toolkit.issues.feature_requests"></a></span><a class="link" href="issues.html#math_toolkit.issues.feature_requests">Feature
- Requests</a>
- </h5>
- <p>
- The following table lists distributions that are found in other packages but
- which are not yet present here, the more frequently the distribution is found,
- the higher the priority for implementing it:
- </p>
- <div class="informaltable"><table class="table">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- <p>
- Distribution
- </p>
- </th>
- <th>
- <p>
- R
- </p>
- </th>
- <th>
- <p>
- Mathematica 6
- </p>
- </th>
- <th>
- <p>
- NIST
- </p>
- </th>
- <th>
- <p>
- Regress+
- </p>
- </th>
- <th>
- <p>
- Matlab
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Geometric
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Multinomial
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Tukey Lambda
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Half Normal / Folded Normal
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Chi
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Gumbel
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Discrete Uniform
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Log Series
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Nakagami (generalised Chi)
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Log Logistic
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Tukey (Studentized range)
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Wilcoxon rank sum
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Wincoxon signed rank
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non-central Beta
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Maxwell
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Beta-Binomial
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Beta-negative Binomial
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Zipf
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Birnbaum-Saunders / Fatigue Life
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Double Exponential
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Power Normal
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Power Lognormal
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Cosine
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Double Gamma
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Double Weibul
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Hyperbolic Secant
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Semicircular
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bradford
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Birr / Fisk
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Reciprocal
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- X
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Kolmogorov Distribution
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- <td>
- <p>
- -
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- <p>
- Also asked for more than once:
- </p>
- <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
- <li class="listitem">
- Add support for interpolated distributions, possibly combine with numeric
- integration and differentiation.
- </li>
- <li class="listitem">
- Add support for bivariate and multivariate distributions: most especially
- the normal.
- </li>
- <li class="listitem">
- Add support for the log of the cdf and pdf: this is mainly a performance
- optimisation since we can avoid some special function calls for some distributions
- by returning the log of the result.
- </li>
- </ul></div>
- </div>
- <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
- <td align="left"></td>
- <td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
- Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
- Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
- Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
- Daryle Walker and Xiaogang Zhang<p>
- Distributed under the Boost Software License, Version 1.0. (See accompanying
- file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
- </p>
- </div></td>
- </tr></table>
- <hr>
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