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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>
29 <p>
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.
37     </p>
38 <p>
39       If you don't see a component listed here, then we don't have any known issues
40       with it.
41     </p>
42 <h5>
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>
45     </h5>
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)
49         </li></ul></div>
50 <h5>
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
53       Beta</a>
54     </h5>
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
57           (medium priority).
58         </li></ul></div>
59 <h5>
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
62       Gamma</a>
63     </h5>
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).
67         </li></ul></div>
68 <h5>
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>
71     </h5>
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
76           not (Low Priority).
77         </li></ul></div>
78 <h5>
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
81       Integrals</a>
82     </h5>
83 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
84 <li class="listitem">
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).]
90         </li>
91 <li class="listitem">
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).
94         </li>
95 <li class="listitem">
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
98           Priority).
99         </li>
100 </ul></div>
101 <h5>
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
104       T Function</a>
105     </h5>
106 <p>
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.
116     </p>
117 <h5>
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
120       distributions</a>
121     </h5>
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?
125         </li></ul></div>
126 <h5>
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
129       Requests</a>
130     </h5>
131 <p>
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>.
133     </p>
134 <p>
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:
138     </p>
139 <div class="informaltable"><table class="table">
140 <colgroup>
141 <col>
142 <col>
143 <col>
144 <col>
145 <col>
146 <col>
147 </colgroup>
148 <thead><tr>
149 <th>
150               <p>
151                 Distribution
152               </p>
153             </th>
154 <th>
155               <p>
156                 R
157               </p>
158             </th>
159 <th>
160               <p>
161                 Mathematica 6
162               </p>
163             </th>
164 <th>
165               <p>
166                 NIST
167               </p>
168             </th>
169 <th>
170               <p>
171                 Regress+
172               </p>
173             </th>
174 <th>
175               <p>
176                 Matlab
177               </p>
178             </th>
179 </tr></thead>
180 <tbody>
181 <tr>
182 <td>
183               <p>
184                 Geometric
185               </p>
186             </td>
187 <td>
188               <p>
189                 X
190               </p>
191             </td>
192 <td>
193               <p>
194                 X
195               </p>
196             </td>
197 <td>
198               <p>
199                 -
200               </p>
201             </td>
202 <td>
203               <p>
204                 -
205               </p>
206             </td>
207 <td>
208               <p>
209                 X
210               </p>
211             </td>
212 </tr>
213 <tr>
214 <td>
215               <p>
216                 Multinomial
217               </p>
218             </td>
219 <td>
220               <p>
221                 X
222               </p>
223             </td>
224 <td>
225               <p>
226                 -
227               </p>
228             </td>
229 <td>
230               <p>
231                 -
232               </p>
233             </td>
234 <td>
235               <p>
236                 -
237               </p>
238             </td>
239 <td>
240               <p>
241                 X
242               </p>
243             </td>
244 </tr>
245 <tr>
246 <td>
247               <p>
248                 Tukey Lambda
249               </p>
250             </td>
251 <td>
252               <p>
253                 X
254               </p>
255             </td>
256 <td>
257               <p>
258                 -
259               </p>
260             </td>
261 <td>
262               <p>
263                 X
264               </p>
265             </td>
266 <td>
267               <p>
268                 -
269               </p>
270             </td>
271 <td>
272               <p>
273                 -
274               </p>
275             </td>
276 </tr>
277 <tr>
278 <td>
279               <p>
280                 Half Normal / Folded Normal
281               </p>
282             </td>
283 <td>
284               <p>
285                 -
286               </p>
287             </td>
288 <td>
289               <p>
290                 X
291               </p>
292             </td>
293 <td>
294               <p>
295                 -
296               </p>
297             </td>
298 <td>
299               <p>
300                 X
301               </p>
302             </td>
303 <td>
304               <p>
305                 -
306               </p>
307             </td>
308 </tr>
309 <tr>
310 <td>
311               <p>
312                 Chi
313               </p>
314             </td>
315 <td>
316               <p>
317                 -
318               </p>
319             </td>
320 <td>
321               <p>
322                 X
323               </p>
324             </td>
325 <td>
326               <p>
327                 -
328               </p>
329             </td>
330 <td>
331               <p>
332                 X
333               </p>
334             </td>
335 <td>
336               <p>
337                 -
338               </p>
339             </td>
340 </tr>
341 <tr>
342 <td>
343               <p>
344                 Gumbel
345               </p>
346             </td>
347 <td>
348               <p>
349                 -
350               </p>
351             </td>
352 <td>
353               <p>
354                 X
355               </p>
356             </td>
357 <td>
358               <p>
359                 -
360               </p>
361             </td>
362 <td>
363               <p>
364                 X
365               </p>
366             </td>
367 <td>
368               <p>
369                 -
370               </p>
371             </td>
372 </tr>
373 <tr>
374 <td>
375               <p>
376                 Discrete Uniform
377               </p>
378             </td>
379 <td>
380               <p>
381                 -
382               </p>
383             </td>
384 <td>
385               <p>
386                 X
387               </p>
388             </td>
389 <td>
390               <p>
391                 -
392               </p>
393             </td>
394 <td>
395               <p>
396                 -
397               </p>
398             </td>
399 <td>
400               <p>
401                 X
402               </p>
403             </td>
404 </tr>
405 <tr>
406 <td>
407               <p>
408                 Log Series
409               </p>
410             </td>
411 <td>
412               <p>
413                 -
414               </p>
415             </td>
416 <td>
417               <p>
418                 X
419               </p>
420             </td>
421 <td>
422               <p>
423                 -
424               </p>
425             </td>
426 <td>
427               <p>
428                 X
429               </p>
430             </td>
431 <td>
432               <p>
433                 -
434               </p>
435             </td>
436 </tr>
437 <tr>
438 <td>
439               <p>
440                 Nakagami (generalised Chi)
441               </p>
442             </td>
443 <td>
444               <p>
445                 -
446               </p>
447             </td>
448 <td>
449               <p>
450                 -
451               </p>
452             </td>
453 <td>
454               <p>
455                 -
456               </p>
457             </td>
458 <td>
459               <p>
460                 X
461               </p>
462             </td>
463 <td>
464               <p>
465                 X
466               </p>
467             </td>
468 </tr>
469 <tr>
470 <td>
471               <p>
472                 Log Logistic
473               </p>
474             </td>
475 <td>
476               <p>
477                 -
478               </p>
479             </td>
480 <td>
481               <p>
482                 -
483               </p>
484             </td>
485 <td>
486               <p>
487                 -
488               </p>
489             </td>
490 <td>
491               <p>
492                 -
493               </p>
494             </td>
495 <td>
496               <p>
497                 X
498               </p>
499             </td>
500 </tr>
501 <tr>
502 <td>
503               <p>
504                 Tukey (Studentized range)
505               </p>
506             </td>
507 <td>
508               <p>
509                 X
510               </p>
511             </td>
512 <td>
513               <p>
514                 -
515               </p>
516             </td>
517 <td>
518               <p>
519                 -
520               </p>
521             </td>
522 <td>
523               <p>
524                 -
525               </p>
526             </td>
527 <td>
528               <p>
529                 -
530               </p>
531             </td>
532 </tr>
533 <tr>
534 <td>
535               <p>
536                 Wilcoxon rank sum
537               </p>
538             </td>
539 <td>
540               <p>
541                 X
542               </p>
543             </td>
544 <td>
545               <p>
546                 -
547               </p>
548             </td>
549 <td>
550               <p>
551                 -
552               </p>
553             </td>
554 <td>
555               <p>
556                 -
557               </p>
558             </td>
559 <td>
560               <p>
561                 -
562               </p>
563             </td>
564 </tr>
565 <tr>
566 <td>
567               <p>
568                 Wincoxon signed rank
569               </p>
570             </td>
571 <td>
572               <p>
573                 X
574               </p>
575             </td>
576 <td>
577               <p>
578                 -
579               </p>
580             </td>
581 <td>
582               <p>
583                 -
584               </p>
585             </td>
586 <td>
587               <p>
588                 -
589               </p>
590             </td>
591 <td>
592               <p>
593                 -
594               </p>
595             </td>
596 </tr>
597 <tr>
598 <td>
599               <p>
600                 Non-central Beta
601               </p>
602             </td>
603 <td>
604               <p>
605                 X
606               </p>
607             </td>
608 <td>
609               <p>
610                 -
611               </p>
612             </td>
613 <td>
614               <p>
615                 -
616               </p>
617             </td>
618 <td>
619               <p>
620                 -
621               </p>
622             </td>
623 <td>
624               <p>
625                 -
626               </p>
627             </td>
628 </tr>
629 <tr>
630 <td>
631               <p>
632                 Maxwell
633               </p>
634             </td>
635 <td>
636               <p>
637                 -
638               </p>
639             </td>
640 <td>
641               <p>
642                 X
643               </p>
644             </td>
645 <td>
646               <p>
647                 -
648               </p>
649             </td>
650 <td>
651               <p>
652                 -
653               </p>
654             </td>
655 <td>
656               <p>
657                 -
658               </p>
659             </td>
660 </tr>
661 <tr>
662 <td>
663               <p>
664                 Beta-Binomial
665               </p>
666             </td>
667 <td>
668               <p>
669                 -
670               </p>
671             </td>
672 <td>
673               <p>
674                 X
675               </p>
676             </td>
677 <td>
678               <p>
679                 -
680               </p>
681             </td>
682 <td>
683               <p>
684                 -
685               </p>
686             </td>
687 <td>
688               <p>
689                 -
690               </p>
691             </td>
692 </tr>
693 <tr>
694 <td>
695               <p>
696                 Beta-negative Binomial
697               </p>
698             </td>
699 <td>
700               <p>
701                 -
702               </p>
703             </td>
704 <td>
705               <p>
706                 X
707               </p>
708             </td>
709 <td>
710               <p>
711                 -
712               </p>
713             </td>
714 <td>
715               <p>
716                 -
717               </p>
718             </td>
719 <td>
720               <p>
721                 -
722               </p>
723             </td>
724 </tr>
725 <tr>
726 <td>
727               <p>
728                 Zipf
729               </p>
730             </td>
731 <td>
732               <p>
733                 -
734               </p>
735             </td>
736 <td>
737               <p>
738                 X
739               </p>
740             </td>
741 <td>
742               <p>
743                 -
744               </p>
745             </td>
746 <td>
747               <p>
748                 -
749               </p>
750             </td>
751 <td>
752               <p>
753                 -
754               </p>
755             </td>
756 </tr>
757 <tr>
758 <td>
759               <p>
760                 Birnbaum-Saunders / Fatigue Life
761               </p>
762             </td>
763 <td>
764               <p>
765                 -
766               </p>
767             </td>
768 <td>
769               <p>
770                 -
771               </p>
772             </td>
773 <td>
774               <p>
775                 X
776               </p>
777             </td>
778 <td>
779               <p>
780                 -
781               </p>
782             </td>
783 <td>
784               <p>
785                 -
786               </p>
787             </td>
788 </tr>
789 <tr>
790 <td>
791               <p>
792                 Double Exponential
793               </p>
794             </td>
795 <td>
796               <p>
797                 -
798               </p>
799             </td>
800 <td>
801               <p>
802                 -
803               </p>
804             </td>
805 <td>
806               <p>
807                 X
808               </p>
809             </td>
810 <td>
811               <p>
812                 -
813               </p>
814             </td>
815 <td>
816               <p>
817                 -
818               </p>
819             </td>
820 </tr>
821 <tr>
822 <td>
823               <p>
824                 Power Normal
825               </p>
826             </td>
827 <td>
828               <p>
829                 -
830               </p>
831             </td>
832 <td>
833               <p>
834                 -
835               </p>
836             </td>
837 <td>
838               <p>
839                 X
840               </p>
841             </td>
842 <td>
843               <p>
844                 -
845               </p>
846             </td>
847 <td>
848               <p>
849                 -
850               </p>
851             </td>
852 </tr>
853 <tr>
854 <td>
855               <p>
856                 Power Lognormal
857               </p>
858             </td>
859 <td>
860               <p>
861                 -
862               </p>
863             </td>
864 <td>
865               <p>
866                 -
867               </p>
868             </td>
869 <td>
870               <p>
871                 X
872               </p>
873             </td>
874 <td>
875               <p>
876                 -
877               </p>
878             </td>
879 <td>
880               <p>
881                 -
882               </p>
883             </td>
884 </tr>
885 <tr>
886 <td>
887               <p>
888                 Cosine
889               </p>
890             </td>
891 <td>
892               <p>
893                 -
894               </p>
895             </td>
896 <td>
897               <p>
898                 -
899               </p>
900             </td>
901 <td>
902               <p>
903                 -
904               </p>
905             </td>
906 <td>
907               <p>
908                 X
909               </p>
910             </td>
911 <td>
912               <p>
913                 -
914               </p>
915             </td>
916 </tr>
917 <tr>
918 <td>
919               <p>
920                 Double Gamma
921               </p>
922             </td>
923 <td>
924               <p>
925                 -
926               </p>
927             </td>
928 <td>
929               <p>
930                 -
931               </p>
932             </td>
933 <td>
934               <p>
935                 -
936               </p>
937             </td>
938 <td>
939               <p>
940                 X
941               </p>
942             </td>
943 <td>
944               <p>
945                 -
946               </p>
947             </td>
948 </tr>
949 <tr>
950 <td>
951               <p>
952                 Double Weibul
953               </p>
954             </td>
955 <td>
956               <p>
957                 -
958               </p>
959             </td>
960 <td>
961               <p>
962                 -
963               </p>
964             </td>
965 <td>
966               <p>
967                 -
968               </p>
969             </td>
970 <td>
971               <p>
972                 X
973               </p>
974             </td>
975 <td>
976               <p>
977                 -
978               </p>
979             </td>
980 </tr>
981 <tr>
982 <td>
983               <p>
984                 Hyperbolic Secant
985               </p>
986             </td>
987 <td>
988               <p>
989                 -
990               </p>
991             </td>
992 <td>
993               <p>
994                 -
995               </p>
996             </td>
997 <td>
998               <p>
999                 -
1000               </p>
1001             </td>
1002 <td>
1003               <p>
1004                 X
1005               </p>
1006             </td>
1007 <td>
1008               <p>
1009                 -
1010               </p>
1011             </td>
1012 </tr>
1013 <tr>
1014 <td>
1015               <p>
1016                 Semicircular
1017               </p>
1018             </td>
1019 <td>
1020               <p>
1021                 -
1022               </p>
1023             </td>
1024 <td>
1025               <p>
1026                 -
1027               </p>
1028             </td>
1029 <td>
1030               <p>
1031                 -
1032               </p>
1033             </td>
1034 <td>
1035               <p>
1036                 X
1037               </p>
1038             </td>
1039 <td>
1040               <p>
1041                 -
1042               </p>
1043             </td>
1044 </tr>
1045 <tr>
1046 <td>
1047               <p>
1048                 Bradford
1049               </p>
1050             </td>
1051 <td>
1052               <p>
1053                 -
1054               </p>
1055             </td>
1056 <td>
1057               <p>
1058                 -
1059               </p>
1060             </td>
1061 <td>
1062               <p>
1063                 -
1064               </p>
1065             </td>
1066 <td>
1067               <p>
1068                 X
1069               </p>
1070             </td>
1071 <td>
1072               <p>
1073                 -
1074               </p>
1075             </td>
1076 </tr>
1077 <tr>
1078 <td>
1079               <p>
1080                 Birr / Fisk
1081               </p>
1082             </td>
1083 <td>
1084               <p>
1085                 -
1086               </p>
1087             </td>
1088 <td>
1089               <p>
1090                 -
1091               </p>
1092             </td>
1093 <td>
1094               <p>
1095                 -
1096               </p>
1097             </td>
1098 <td>
1099               <p>
1100                 X
1101               </p>
1102             </td>
1103 <td>
1104               <p>
1105                 -
1106               </p>
1107             </td>
1108 </tr>
1109 <tr>
1110 <td>
1111               <p>
1112                 Reciprocal
1113               </p>
1114             </td>
1115 <td>
1116               <p>
1117                 -
1118               </p>
1119             </td>
1120 <td>
1121               <p>
1122                 -
1123               </p>
1124             </td>
1125 <td>
1126               <p>
1127                 -
1128               </p>
1129             </td>
1130 <td>
1131               <p>
1132                 X
1133               </p>
1134             </td>
1135 <td>
1136               <p>
1137                 -
1138               </p>
1139             </td>
1140 </tr>
1141 <tr>
1142 <td>
1143               <p>
1144                 Kolmogorov Distribution
1145               </p>
1146             </td>
1147 <td>
1148               <p>
1149                 -
1150               </p>
1151             </td>
1152 <td>
1153               <p>
1154                 -
1155               </p>
1156             </td>
1157 <td>
1158               <p>
1159                 -
1160               </p>
1161             </td>
1162 <td>
1163               <p>
1164                 -
1165               </p>
1166             </td>
1167 <td>
1168               <p>
1169                 -
1170               </p>
1171             </td>
1172 </tr>
1173 </tbody>
1174 </table></div>
1175 <p>
1176       Also asked for more than once:
1177     </p>
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.
1182         </li>
1183 <li class="listitem">
1184           Add support for bivariate and multivariate distributions: most especially
1185           the normal.
1186         </li>
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.
1191         </li>
1192 </ul></div>
1193 </div>
1194 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
1195 <td align="left"></td>
1196 <td align="right"><div class="copyright-footer">Copyright &#169; 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 R&#229;de, 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>)
1202       </p>
1203 </div></td>
1204 </tr></table>
1205 <hr>
1206 <div class="spirit-nav">
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