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26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
27 <a name="math_toolkit.issues"></a><a class="link" href="issues.html" title="Known Issues, and TODO List">Known Issues, and TODO List</a>
28 </h2></div></div></div>
30 Predominantly this is a TODO list, or a list of possible future enhancements.
31 Items labled "High Priority" effect the proper functioning of the
32 component, and should be fixed as soon as possible. Items labled "Medium
33 Priority" are desirable enhancements, often pertaining to the performance
34 of the component, but do not effect it's accuracy or functionality. Items labled
35 "Low Priority" should probably be investigated at some point. Such
36 classifications are obviously highly subjective.
39 If you don't see a component listed here, then we don't have any known issues
43 <a name="math_toolkit.issues.h0"></a>
44 <span class="phrase"><a name="math_toolkit.issues.tgamma"></a></span><a class="link" href="issues.html#math_toolkit.issues.tgamma">tgamma</a>
46 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
47 Can the <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
48 be optimized any further? (low priority)
51 <a name="math_toolkit.issues.h1"></a>
52 <span class="phrase"><a name="math_toolkit.issues.incomplete_beta"></a></span><a class="link" href="issues.html#math_toolkit.issues.incomplete_beta">Incomplete
55 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
56 Investigate Didonato and Morris' asymptotic expansion for large a and b
60 <a name="math_toolkit.issues.h2"></a>
61 <span class="phrase"><a name="math_toolkit.issues.inverse_gamma"></a></span><a class="link" href="issues.html#math_toolkit.issues.inverse_gamma">Inverse
64 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
65 Investigate whether we can skip iteration altogether if the first approximation
66 is good enough (Medium Priority).
69 <a name="math_toolkit.issues.h3"></a>
70 <span class="phrase"><a name="math_toolkit.issues.polynomials"></a></span><a class="link" href="issues.html#math_toolkit.issues.polynomials">Polynomials</a>
72 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
73 The Legendre and Laguerre Polynomials have surprisingly different error
74 rates on different platforms, considering they are evaluated with only
75 basic arithmetic operations. Maybe this is telling us something, or maybe
79 <a name="math_toolkit.issues.h4"></a>
80 <span class="phrase"><a name="math_toolkit.issues.elliptic_integrals"></a></span><a class="link" href="issues.html#math_toolkit.issues.elliptic_integrals">Elliptic
83 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
85 [para Carlson's algorithms (mainly R<sub>J</sub>) are somewhat prone to internal overflow/underflow
86 when the arguments are very large or small. The homogeneity relations:]
87 [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,
88 kr) = k<sup>-3/2</sup> R<sub>J</sub>(a, b, c, r)] [para could be used to sidestep trouble here:
89 provided the problem domains can be accurately identified. (Medium Priority).]
92 There are a several other integrals: Bulirsch's <span class="emphasis"><em>el</em></span>
93 functions that could be implemented using Carlson's integrals (Low Priority).
96 The integrals K(k) and E(k) could be implemented using rational approximations
97 (both for efficiency and accuracy), assuming we can find them. (Medium
102 <a name="math_toolkit.issues.h5"></a>
103 <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
107 There is a problem area at arbitrary precision when <span class="emphasis"><em>a</em></span>
108 is very close to 1. However, note that the value for <span class="emphasis"><em>T(h, 1)</em></span>
109 is well known and easy to compute, and if we replaced the <span class="emphasis"><em>a<sup>k</sup></em></span>
110 terms in series T1, T2 or T4 by <span class="emphasis"><em>(a<sup>k</sup> - 1)</em></span> then we would
111 have the difference between <span class="emphasis"><em>T(h, a)</em></span> and <span class="emphasis"><em>T(h,
112 1)</em></span>. Unfortunately this doesn't improve the convergence of those
113 series in that area. It certainly looks as though a new series in terms of
114 <span class="emphasis"><em>(1-a)<sup>k</sup></em></span> is both possible and desirable in this area, but
115 it remains elusive at present.
118 <a name="math_toolkit.issues.h6"></a>
119 <span class="phrase"><a name="math_toolkit.issues.statistical_distributions"></a></span><a class="link" href="issues.html#math_toolkit.issues.statistical_distributions">Statistical
122 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
123 Student's t Perhaps switch to normal distribution as a better approximation
124 for very large degrees of freedom?
127 <a name="math_toolkit.issues.h7"></a>
128 <span class="phrase"><a name="math_toolkit.issues.feature_requests"></a></span><a class="link" href="issues.html#math_toolkit.issues.feature_requests">Feature
132 We have a request for the Lambert W function, see <a href="https://svn.boost.org/trac/boost/ticket/11027" target="_top">#11027</a>.
135 The following table lists distributions that are found in other packages but
136 which are not yet present here, the more frequently the distribution is found,
137 the higher the priority for implementing it:
139 <div class="informaltable"><table class="table">
280 Half Normal / Folded Normal
440 Nakagami (generalised Chi)
504 Tukey (Studentized range)
696 Beta-negative Binomial
760 Birnbaum-Saunders / Fatigue Life
1144 Kolmogorov Distribution
1176 Also asked for more than once:
1178 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1179 <li class="listitem">
1180 Add support for interpolated distributions, possibly combine with numeric
1181 integration and differentiation.
1183 <li class="listitem">
1184 Add support for bivariate and multivariate distributions: most especially
1187 <li class="listitem">
1188 Add support for the log of the cdf and pdf: this is mainly a performance
1189 optimisation since we can avoid some special function calls for some distributions
1190 by returning the log of the result.
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1196 <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
1197 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
1198 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
1199 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
1200 Distributed under the Boost Software License, Version 1.0. (See accompanying
1201 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>)
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