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| <div class="section" lang="en"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="math_toolkit.status.issues"></a><a class="link" href="issues.html" title="Known Issues, and Todo List"> Known Issues, and Todo List</a> |
| </h3></div></div></div> |
| <p> |
| This section lists those issues that are known about. |
| </p> |
| <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> |
| <a name="math_toolkit.status.issues.tgamma"></a><h5> |
| <a name="id1293781"></a> |
| <a class="link" href="issues.html#math_toolkit.status.issues.tgamma">tgamma</a> |
| </h5> |
| <div class="itemizedlist"><ul type="disc"><li> |
| Can the <a class="link" href="../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a> |
| be optimized any further? (low priority) |
| </li></ul></div> |
| <a name="math_toolkit.status.issues.incomplete_beta"></a><h5> |
| <a name="id1293810"></a> |
| <a class="link" href="issues.html#math_toolkit.status.issues.incomplete_beta">Incomplete Beta</a> |
| </h5> |
| <div class="itemizedlist"><ul type="disc"><li> |
| Investigate Didonato and Morris' asymptotic expansion for large a and |
| b (medium priority). |
| </li></ul></div> |
| <a name="math_toolkit.status.issues.inverse_gamma"></a><h5> |
| <a name="id1293834"></a> |
| <a class="link" href="issues.html#math_toolkit.status.issues.inverse_gamma">Inverse Gamma</a> |
| </h5> |
| <div class="itemizedlist"><ul type="disc"><li> |
| Investigate whether we can skip iteration altogether if the first approximation |
| is good enough (Medium Priority). |
| </li></ul></div> |
| <a name="math_toolkit.status.issues.polynomials"></a><h5> |
| <a name="id1293858"></a> |
| <a class="link" href="issues.html#math_toolkit.status.issues.polynomials">Polynomials</a> |
| </h5> |
| <div class="itemizedlist"><ul type="disc"><li> |
| 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> |
| <a name="math_toolkit.status.issues.elliptic_integrals"></a><h5> |
| <a name="id1293882"></a> |
| <a class="link" href="issues.html#math_toolkit.status.issues.elliptic_integrals">Elliptic Integrals</a> |
| </h5> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| Carlson's algorithms are essentially unchanged from Xiaogang Zhang's |
| Google Summer of Code student project, and are based on Carlson's original |
| papers. However, Carlson has revised his algorithms since then (refer |
| to the references in the elliptic integral docs for a list), to improve |
| performance and accuracy, we may be able to take advantage of these improvements |
| too (Low Priority). |
| </li> |
| <li> |
| <p>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:</p> |
| <p>R<sub>F</sub>(ka, |
| kb, kc) = k<sup>-1/2</sup> R<sub>F</sub>(a, b, c)</p> |
| <p>and</p> |
| <p>R<sub>J</sub>(ka, kb, kc, kr) = k<sup>-3/2</sup> R<sub>J</sub>(a, b, c, r)</p> |
| <p>could |
| be used to sidestep trouble here: provided the problem domains can be |
| accurately identified. (Medium Priority).</p> |
| |
| </li> |
| <li> |
| Carlson's R<sub>C</sub> can be reduced to elementary funtions (asin and log), would |
| it be more efficient evaluated this way, rather than by Carlson's algorithms? |
| (Low Priority). |
| </li> |
| <li> |
| Should we add an implementation of Carlson's R<sub>G</sub>? It's not required for |
| the Legendre form integrals, but some people may find it useful (Low |
| Priority). |
| </li> |
| <li> |
| There are a several other integrals: D(φ, k), Z(β, k), Λ<sub>0</sub>(β, k) and Bulirsch's |
| <span class="emphasis"><em>el</em></span> functions that could be implemented using Carlson's |
| integrals (Low Priority). |
| </li> |
| <li> |
| 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> |
| <li> |
| There is a sub-domain of <a class="link" href="../special/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a> |
| that is unimplemented (see the docs for details), currently it's not |
| clear how to solve this issue, or if it's ever likely to be an real problem |
| in practice - especially as most other implementations don't support |
| this domain either (Medium Priority). |
| </li> |
| </ul></div> |
| <a name="math_toolkit.status.issues.inverse_hyperbolic_functions"></a><h5> |
| <a name="id1294013"></a> |
| <a class="link" href="issues.html#math_toolkit.status.issues.inverse_hyperbolic_functions">Inverse |
| Hyperbolic Functions</a> |
| </h5> |
| <div class="itemizedlist"><ul type="disc"><li> |
| These functions are inherited from previous Boost versions, before <a class="link" href="../special/powers/log1p.html" title="log1p">log1p</a> became widely |
| available. Would they be better expressed in terms of this function? |
| This is probably only an issue for very high precision types (Low Priority). |
| </li></ul></div> |
| <a name="math_toolkit.status.issues.statistical_distributions"></a><h5> |
| <a name="id1294042"></a> |
| <a class="link" href="issues.html#math_toolkit.status.issues.statistical_distributions">Statistical |
| distributions</a> |
| </h5> |
| <div class="itemizedlist"><ul type="disc"><li> |
| Student's t Perhaps switch to normal distribution as a better approximation |
| for very large degrees of freedom? |
| </li></ul></div> |
| <a name="math_toolkit.status.issues.feature_requests"></a><h5> |
| <a name="id1294066"></a> |
| <a class="link" href="issues.html#math_toolkit.status.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> |
| Inverse Gausian / Inverse Normal |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| <td> |
| <p> |
| X |
| </p> |
| </td> |
| <td> |
| <p> |
| - |
| </p> |
| </td> |
| <td> |
| <p> |
| X |
| </p> |
| </td> |
| <td> |
| <p> |
| X |
| </p> |
| </td> |
| </tr> |
| <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> |
| Laplace |
| </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> |
| 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> |
| </tbody> |
| </table></div> |
| <p> |
| Also asked for more than once: |
| </p> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| Add support for interpolated distributions, possibly combine with numeric |
| integration and differentiation. |
| </li> |
| <li> |
| Add support for bivariate and multivariate distributions: most especially |
| the normal. |
| </li> |
| <li> |
| 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 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<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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