Changeset 88

docs/alloc.html

r87	r88
798	798	Page was generated with
799	799	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
800		on ~~Tue Oct 13 20:16:25~~ 2009
	800	on Sun Oct 18 13:42:20 2009
801	801
802	802	</td></tr>

docs/base.html

r87	r88
266	266	<font color=blue>assert</font>(s == [0, 1, 2, 3, 4]);
267	267	</pre>
	268
268	269	<br><br>
269	270
…	…
404	405
405	406
406		<dd>No, nothing this horribly inefficient is used internally.
407		A struct that generates all possible permutations of a sequence,
	407	<dd>A struct that generates all possible permutations of a sequence,
408	408	and can be iterated over with foreach. Note that permutations are
409	409	output in undefined order. Also note that the returned permutations
…	…
427	427	<font color=blue>assert</font>(res.length == 6);
428	428	</pre>
	429
429	430	<br><br>
430	431
…	…
508	509	<font color=blue>auto</font> p = <u>perm</u>(5); <font color=green>// Permutations of integers on range [0, 5].
509	510	</font> <font color=blue>auto</font> p = <u>perm</u>(-1, 2); <font color=green>// Permutations of integers on range [-1, 2].
510		~~</font></pre>~~
511
512		~~<br><br>~~
513
514		~~</dd>~~
515
516		~~<script>explorer.outline.writeEnabled = true;</script>~~
517		~~<dt><span class="decl">CombRet!(T)~~
518		~~<span class="currsymbol">comb</span>~~
519		~~<script>explorer.outline.addDecl('comb');</script>~~
520
521		~~(T)(T <span class="funcparam">stuff</span>, uint <span class="funcparam">r</span>);~~
522		~~</span></dt>~~
523		~~<script>explorer.outline.writeEnabled = false;</script>~~
524
525
526		~~<dd>Create a Comb struct from a range or of a set of bounds.~~
527		~~<br><br>~~
528		~~<b>Note:</b><br>~~
529		~~CombRet is just a template to figure out what this should return.~~
530		~~I would use auto if not for bug 2251.~~
531
532		~~<br><br>~~
533		~~<b>Examples:</b><br>~~
534		~~<pre class="d_code"> <font color=blue>auto</font> p = <u>comb</u>([1,2,3]);~~
535		~~<font color=blue>auto</font> p = <u>comb</u>(5); <font color=green>// Permutations of integers on range [0, 5].~~
536	511	</font></pre>
537	512
…	…
653	628
654	629	<script>explorer.outline.writeEnabled = true;</script>
	630	<dt><span class="decl">CombRet!(T)
	631	<span class="currsymbol">comb</span>
	632	<script>explorer.outline.addDecl('comb');</script>
	633
	634	(T)(T <span class="funcparam">stuff</span>, uint <span class="funcparam">r</span>);
	635	</span></dt>
	636	<script>explorer.outline.writeEnabled = false;</script>
	637
	638
	639	<dd>Create a Comb struct from a range or of a set of bounds.
	640	<br><br>
	641	<b>Note:</b><br>
	642	CombRet is just a template to figure out what this should return.
	643	I would use auto if not for bug 2251.
	644
	645	<br><br>
	646	<b>Examples:</b><br>
	647	<pre class="d_code"> <font color=blue>auto</font> p = <u>comb</u>([1,2,3]);
	648	<font color=blue>auto</font> p = <u>comb</u>(5); <font color=green>// Permutations of integers on range [0, 5].
	649	</font></pre>
	650
	651	<br><br>
	652
	653	</dd>
	654
	655	<script>explorer.outline.writeEnabled = true;</script>
655	656	<dt><span class="decl">T[]
656	657	<span class="currsymbol">intersect</span>
…	…
807	808	Page was generated with
808	809	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
809		on ~~Tue Oct 13 20:16:25~~ 2009
	810	on Sun Oct 18 13:42:20 2009
810	811
811	812	</td></tr>

docs/cor.html

r87	r88
24	24	<dl>
25	25	<script>explorer.outline.writeEnabled = true;</script>
26		<dt><span class="decl">~~real~~
	26	<dt><span class="decl">Pcor
27	27	<span class="currsymbol">pcor</span>
28	28	<script>explorer.outline.addDecl('pcor');</script>
…	…
33	33
34	34
35		<dd>Pearson correlation. When the term correlation is used unqualified, it is
	35	<dd>Convenience function for calculating Pearson correlation.
	36	When the term correlation is used unqualified, it is
36	37	usually referring to this quantity. This is a parametric correlation
37	38	metric and should not be used with extremely ill-behaved data.
…	…
39	40	lengths, it uses the first min(input1.length, input2.length) elements.
40	41	<br><br>
	42	<b>Note:</b><br>
	43	The Pcor struct returned by this function is alias this'd to the
	44	correlation coefficient. Therefore, the result from this function can
	45	be treated simply as a floating point number.
	46
	47	<br><br>
41	48
42	49	</dd>
…	…
44	51	<script>explorer.outline.writeEnabled = true;</script>
45	52	<dt><span class="decl">struct
46		<span class="currsymbol">~~Online~~Pcor</span>
47		<script>explorer.outline.addDecl('~~Online~~Pcor');</script>
	53	<span class="currsymbol">Pcor</span>
	54	<script>explorer.outline.addDecl('Pcor');</script>
48	55
49	56	;
…	…
58	65	<br><br>
59	66
	67	<span class="currsymbol">Pcor</span>
	68	<script>explorer.outline.addDecl('Pcor');</script>
	69
	70	.cor is alias this'd, so if this struct is used as a real, it will
	71	be converted to a simple correlation coefficient automatically.
	72
	73	<br><br>
	74
60	75
61	76	<script>explorer.outline.incSymbolLevel();</script>
…	…
274	289	Page was generated with
275	290	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
276		on ~~Tue Oct 13 20:16:25~~ 2009
	291	on Sun Oct 18 13:42:20 2009
277	292
278	293	</td></tr>

docs/distrib.html

r87	r88
572	572
573	573	(real <span class="funcparam">x</span>, real <span class="funcparam">df1</span>, real <span class="funcparam">df2</span>);
574		~~<br>real~~
575		~~<span class="currsymbol">invFisherCDFR</span>~~
576		~~<script>explorer.outline.addDecl('invFisherCDFR');</script>~~
577
578		~~(real <span class="funcparam">df1</span>, real <span class="funcparam">df2</span>, real <span class="funcparam">p</span>);~~
579	574	</span></dt>
580	575	<script>explorer.outline.writeEnabled = false;</script>
…	…
626	621	<script>explorer.outline.writeEnabled = true;</script>
627	622	<dt><span class="decl">real
	623	<span class="currsymbol">invFisherCDFR</span>
	624	<script>explorer.outline.addDecl('invFisherCDFR');</script>
	625
	626	(real <span class="funcparam">df1</span>, real <span class="funcparam">df2</span>, real <span class="funcparam">p</span>);
	627	</span></dt>
	628	<script>explorer.outline.writeEnabled = false;</script>
	629
	630
	631	<dd>Inverse of complemented Fisher distribution
	632	<br><br>
	633	Finds the F density argument x such that the integral
	634	from x to infinity of the F density is equal to the
	635	given probability <span class="funcparam">p</span>.
	636	<br><br>
	637
	638	This is accomplished using the inverse beta integral
	639	function and the relations
	640	<br><br>
	641
	642	z = betaIncompleteInv( <span class="funcparam">df2</span>/2, <span class="funcparam">df1</span>/2, <span class="funcparam">p</span> ),
	643	x = <span class="funcparam">df2</span> (1-z) / (<span class="funcparam">df1</span> z).
	644	<br><br>
	645
	646	Note that the following relations hold for the inverse of
	647	the uncomplemented F distribution:
	648	<br><br>
	649
	650	z = betaIncompleteInv( <span class="funcparam">df1</span>/2, <span class="funcparam">df2</span>/2, <span class="funcparam">p</span> ),
	651	x = <span class="funcparam">df2</span> z / (<span class="funcparam">df1</span> (1-z)).
	652	ditto
	653	<br><br>
	654
	655	</dd>
	656
	657	<script>explorer.outline.writeEnabled = true;</script>
	658	<dt><span class="decl">real
628	659	<span class="currsymbol">negBinomPMF</span>
629	660	<script>explorer.outline.addDecl('negBinomPMF');</script>
…	…
810	841	<script>explorer.outline.writeEnabled = true;</script>
811	842	<dt><span class="decl">pure nothrow real
	843	<span class="currsymbol">laplacePDF</span>
	844	<script>explorer.outline.addDecl('laplacePDF');</script>
	845
	846	(real <span class="funcparam">x</span>, real <span class="funcparam">mu</span> = 0, real <span class="funcparam">b</span> = 1);
	847	</span></dt>
	848	<script>explorer.outline.writeEnabled = false;</script>
	849
	850
	851	<dd><br><br>
	852	</dd>
	853
	854	<script>explorer.outline.writeEnabled = true;</script>
	855	<dt><span class="decl">pure nothrow real
812	856	<span class="currsymbol">laplaceCDF</span>
813	857	<script>explorer.outline.addDecl('laplaceCDF');</script>
…	…
869	913	Page was generated with
870	914	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
871		on ~~Tue Oct 13 20:16:26~~ 2009
	915	on Sun Oct 18 13:42:20 2009
872	916
873	917	</td></tr>

docs/gamma.html

r87	r88
242	242	Page was generated with
243	243	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
244		on ~~Tue Oct 13 20:16:26~~ 2009
	244	on Sun Oct 18 13:42:20 2009
245	245
246	246	</td></tr>

docs/infotheory.html

r87	r88
208	208	Page was generated with
209	209	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
210		on ~~Tue Oct 13 20:16:26~~ 2009
	210	on Sun Oct 18 13:42:20 2009
211	211
212	212	</td></tr>

docs/random.html

r87	r88
312	312	Page was generated with
313	313	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
314		on ~~Tue Oct 13 20:16:26~~ 2009
	314	on Sun Oct 18 13:42:20 2009
315	315
316	316	</td></tr>

docs/regress.html

r87	r88
408	408	Page was generated with
409	409	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
410		on ~~Tue Oct 13 20:16:26~~ 2009
	410	on Sun Oct 18 13:42:20 2009
411	411
412	412	</td></tr>

docs/sort.html

r87	r88
406	406	Page was generated with
407	407	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
408		on ~~Tue Oct 13 20:16:26~~ 2009
	408	on Sun Oct 18 13:42:21 2009
409	409
410	410	</td></tr>

docs/stats.html

r87	r88
21	21	Page was generated with
22	22	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
23		on ~~Tue Oct 13 20:16:26~~ 2009
	23	on Sun Oct 18 13:42:21 2009
24	24
25	25	</td></tr>

docs/summary.html

r87	r88
127	127	<script>explorer.outline.writeEnabled = true;</script>
128	128	<dt><span class="decl">struct
129		<span class="currsymbol">~~Online~~Mean</span>
130		<script>explorer.outline.addDecl('~~Online~~Mean');</script>
	129	<span class="currsymbol">Mean</span>
	130	<script>explorer.outline.addDecl('Mean');</script>
131	131
132	132	;
…	…
140	140	<br><br>
141	141	<b>Examples:</b><br>
142		<pre class="d_code"> <u>~~Online~~Mean</u> summ;
	142	<pre class="d_code"> <u>Mean</u> summ;
143	143	summ.put(1);
144	144	summ.put(2);
…	…
214	214	<script>explorer.outline.writeEnabled = true;</script>
215	215	<dt><span class="decl">struct
216		<span class="currsymbol">~~Online~~GeometricMean</span>
217		<script>explorer.outline.addDecl('~~Online~~GeometricMean');</script>
	216	<span class="currsymbol">GeometricMean</span>
	217	<script>explorer.outline.addDecl('GeometricMean');</script>
218	218
219	219	;
…	…
320	320	<script>explorer.outline.writeEnabled = true;</script>
321	321	<dt><span class="decl">struct
322		<span class="currsymbol">~~Online~~MeanSD</span>
323		<script>explorer.outline.addDecl('~~Online~~MeanSD');</script>
	322	<span class="currsymbol">MeanSD</span>
	323	<script>explorer.outline.addDecl('MeanSD');</script>
324	324
325	325	;
…	…
331	331	for stdev, var cost a few floating point ops. Getter for mean costs
332	332	a single branch to check for N == 0. Relatively expensive floating point
333		ops, if you only need mean, try ~~Online~~Mean. This struct uses O(1) space and
	333	ops, if you only need mean, try Mean. This struct uses O(1) space and
334	334	does NOT store the individual elements.
335	335	<br><br>
336	336	<b>Examples:</b><br>
337		<pre class="d_code"> <u>~~Online~~MeanSD</u> summ;
	337	<pre class="d_code"> <u>MeanSD</u> summ;
338	338	summ.put(1);
339	339	summ.put(2);
…	…
434	434
435	435	<script>explorer.outline.writeEnabled = true;</script>
436		<dt><span class="decl">struct
437		<span class="currsymbol">MeanSD</span>
438		<script>explorer.outline.addDecl('MeanSD');</script>
439
440		;
441		</span></dt>
442		<script>explorer.outline.writeEnabled = false;</script>
443
444
445		<dd>Simple holder for mean, stdev/variance. Plain old data, accessing is
446		cheap.
447		<br><br>
448
449
450		<script>explorer.outline.incSymbolLevel();</script>
451		<dl>
452		<script>explorer.outline.writeEnabled = true;</script>
453		<dt><span class="decl">real
454		<span class="currsymbol">mean</span>
455		<script>explorer.outline.addDecl('mean');</script>
456
457		;
458		</span></dt>
459		<script>explorer.outline.writeEnabled = false;</script>
460
461
462		<dd><br><br>
463		</dd>
464
465		<script>explorer.outline.writeEnabled = true;</script>
466		<dt><span class="decl">real
467		<span class="currsymbol">SD</span>
468		<script>explorer.outline.addDecl('SD');</script>
469
470		;
471		</span></dt>
472		<script>explorer.outline.writeEnabled = false;</script>
473
474
475		<dd><br><br>
476		</dd>
477		</dl>
478		<script>explorer.outline.decSymbolLevel();</script>
479
	436	<dt><span class="decl">MeanSD
	437	<span class="currsymbol">meanStdev</span>
	438	<script>explorer.outline.addDecl('meanStdev');</script>
	439
	440	(T)(T <span class="funcparam">data</span>);
	441	</span></dt>
	442	<script>explorer.outline.writeEnabled = false;</script>
	443
	444
	445	<dd>Convenience function that puts all elements of data into a MeanSD struct,
	446	then returns this struct.
	447	<br><br>
480	448
481	449	</dd>
…	…
502	470
503	471	<script>explorer.outline.writeEnabled = true;</script>
504		~~<dt><span class="decl">MeanSD~~
505		~~<span class="currsymbol">meanVariance</span>~~
506		~~<script>explorer.outline.addDecl('meanVariance');</script>~~
507
508		~~(T)(T <span class="funcparam">data</span>);~~
509		~~</span></dt>~~
510		~~<script>explorer.outline.writeEnabled = false;</script>~~
511
512
513		~~<dd>Calculates both mean and variance of an input range, returns a MeanSD~~
514		~~struct.~~
515		~~<br><br>~~
516
517		~~</dd>~~
518
519		~~<script>explorer.outline.writeEnabled = true;</script>~~
520		~~<dt><span class="decl">MeanSD~~
521		~~<span class="currsymbol">meanStdev</span>~~
522		~~<script>explorer.outline.addDecl('meanStdev');</script>~~
523
524		~~(T)(T <span class="funcparam">data</span>);~~
525		~~</span></dt>~~
526		~~<script>explorer.outline.writeEnabled = false;</script>~~
527
528
529		~~<dd>Calculates both mean and standard deviation of an input range, returns a~~
530		~~MeanSD struct.~~
531		~~<br><br>~~
532
533		~~</dd>~~
534
535		~~<script>explorer.outline.writeEnabled = true;</script>~~
536	472	<dt><span class="decl">real
537	473	<span class="currsymbol">stdev</span>
…	…
551	487	<script>explorer.outline.writeEnabled = true;</script>
552	488	<dt><span class="decl">struct
553		<span class="currsymbol">~~Online~~Summary</span>
554		<script>explorer.outline.addDecl('~~Online~~Summary');</script>
	489	<span class="currsymbol">Summary</span>
	490	<script>explorer.outline.addDecl('Summary');</script>
555	491
556	492	;
…	…
561	497	<dd>Output range to compute mean, stdev, variance, skewness, kurtosis, min, and
562	498	max online. Using this struct is relatively expensive, so if you just need
563		mean and/or stdev, try ~~OnlineMeanSD or Online~~Mean. Getter methods for stdev,
	499	mean and/or stdev, try MeanSD or Mean. Getter methods for stdev,
564	500	var cost a few floating point ops. Getter for mean costs a single branch to
565	501	check for N == 0. Getters for skewness and kurtosis cost a whole bunch of
…	…
568	504	<br><br>
569	505	<b>Examples:</b><br>
570		<pre class="d_code"> <u>~~Online~~Summary</u> summ;
	506	<pre class="d_code"> <u>Summary</u> summ;
571	507	summ.put(1);
572	508	summ.put(2);
…	…
789	725
790	726	<script>explorer.outline.writeEnabled = true;</script>
791		~~<dt><span class="decl">struct~~
792		~~<span class="currsymbol">Summary</span>~~
793		~~<script>explorer.outline.addDecl('Summary');</script>~~
794
795		;
796		~~</span></dt>~~
797		~~<script>explorer.outline.writeEnabled = false;</script>~~
798
799
800		~~<dd>Plain old data struct for holding results of summary(). Accessing members~~
801		~~is cheap.~~
802		~~<br><br>~~
803
804
805		~~<script>explorer.outline.incSymbolLevel();</script>~~
806		~~<dl>~~
807		~~<script>explorer.outline.writeEnabled = true;</script>~~
808		~~<dt><span class="decl">ulong~~
809		~~<span class="currsymbol">N</span>~~
810		~~<script>explorer.outline.addDecl('N');</script>~~
811
812		;
813		~~</span></dt>~~
814		~~<script>explorer.outline.writeEnabled = false;</script>~~
815
816
817		~~<dd><br><br>~~
818		~~</dd>~~
819
820		~~<script>explorer.outline.writeEnabled = true;</script>~~
821		~~<dt><span class="decl">real~~
822		~~<span class="currsymbol">mean</span>~~
823		~~<script>explorer.outline.addDecl('mean');</script>~~
824
825		;
826		~~</span></dt>~~
827		~~<script>explorer.outline.writeEnabled = false;</script>~~
828
829
830		~~<dd><br><br>~~
831		~~</dd>~~
832
833		~~<script>explorer.outline.writeEnabled = true;</script>~~
834		~~<dt><span class="decl">real~~
835		~~<span class="currsymbol">var</span>~~
836		~~<script>explorer.outline.addDecl('var');</script>~~
837
838		;
839		~~</span></dt>~~
840		~~<script>explorer.outline.writeEnabled = false;</script>~~
841
842
843		~~<dd><br><br>~~
844		~~</dd>~~
845
846		~~<script>explorer.outline.writeEnabled = true;</script>~~
847		~~<dt><span class="decl">real~~
848		~~<span class="currsymbol">SD</span>~~
849		~~<script>explorer.outline.addDecl('SD');</script>~~
850
851		;
852		~~</span></dt>~~
853		~~<script>explorer.outline.writeEnabled = false;</script>~~
854
855
856		~~<dd><br><br>~~
857		~~</dd>~~
858
859		~~<script>explorer.outline.writeEnabled = true;</script>~~
860		~~<dt><span class="decl">real~~
861		~~<span class="currsymbol">skew</span>~~
862		~~<script>explorer.outline.addDecl('skew');</script>~~
863
864		;
865		~~</span></dt>~~
866		~~<script>explorer.outline.writeEnabled = false;</script>~~
867
868
869		~~<dd><br><br>~~
870		~~</dd>~~
871
872		~~<script>explorer.outline.writeEnabled = true;</script>~~
873		~~<dt><span class="decl">real~~
874		~~<span class="currsymbol">kurtosis</span>~~
875		~~<script>explorer.outline.addDecl('kurtosis');</script>~~
876
877		;
878		~~</span></dt>~~
879		~~<script>explorer.outline.writeEnabled = false;</script>~~
880
881
882		~~<dd><br><br>~~
883		~~</dd>~~
884
885		~~<script>explorer.outline.writeEnabled = true;</script>~~
886		~~<dt><span class="decl">real~~
887		~~<span class="currsymbol">min</span>~~
888		~~<script>explorer.outline.addDecl('min');</script>~~
889
890		;
891		~~</span></dt>~~
892		~~<script>explorer.outline.writeEnabled = false;</script>~~
893
894
895		~~<dd><br><br>~~
896		~~</dd>~~
897
898		~~<script>explorer.outline.writeEnabled = true;</script>~~
899		~~<dt><span class="decl">real~~
900		~~<span class="currsymbol">max</span>~~
901		~~<script>explorer.outline.addDecl('max');</script>~~
902
903		;
904		~~</span></dt>~~
905		~~<script>explorer.outline.writeEnabled = false;</script>~~
906
907
908		~~<dd><br><br>~~
909		~~</dd>~~
910
911		~~<script>explorer.outline.writeEnabled = true;</script>~~
912		~~<dt><span class="decl">string~~
913		~~<span class="currsymbol">toString</span>~~
914		~~<script>explorer.outline.addDecl('toString');</script>~~
915
916		~~();~~
917		~~</span></dt>~~
918		~~<script>explorer.outline.writeEnabled = false;</script>~~
919
920
921		~~<dd><br><br>~~
922		~~</dd>~~
923		~~</dl>~~
924		~~<script>explorer.outline.decSymbolLevel();</script>~~
925
926
927		~~</dd>~~
928
929		~~<script>explorer.outline.writeEnabled = true;</script>~~
930	727	<dt><span class="decl">Summary
931	728	<span class="currsymbol">summary</span>
…	…
937	734
938	735
939		<dd>Calculates all
940		<span class="currsymbol">summary</span>
941		<script>explorer.outline.addDecl('summary');</script>
942
943		stats (mean, variance, standard dev., skewness
944		and kurtosis) on an input range with elements that can be implicitly
945		converted to real. Returns the results in a Summary struct.
	736	<dd>Convenience function. Puts all elements of data into a Summary struct,
	737	and returns this struct.
946	738	<br><br>
947	739
…	…
1116	908	Page was generated with
1117	909	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
1118		on ~~Tue Oct 13 20:16:26~~ 2009
	910	on Sun Oct 18 13:42:21 2009
1119	911
1120	912	</td></tr>

docs/tests.html

r87	r88
247	247
248	248	<script>explorer.outline.writeEnabled = true;</script>
	249	<dt><span class="decl">template
	250	<span class="currsymbol">isSummary</span>
	251	<script>explorer.outline.addDecl('isSummary');</script>
	252
	253	(T)</span></dt>
	254	<script>explorer.outline.writeEnabled = false;</script>
	255
	256
	257	<dd>Tests whether a struct/class has the necessary information for calculating
	258	a T-test. It must have a property .mean (mean), .stdev (stdandard deviation),
	259	.var (variance), and .N (sample size).
	260
	261	<br><br>
	262
	263	</dd>
	264
	265	<script>explorer.outline.writeEnabled = true;</script>
249	266	<dt><span class="decl">ConfInt
250	267	<span class="currsymbol">studentsTTest</span>
…	…
264	281	A ConfInt containing T, the P-value and the boundaries of
265	282	the confidence interval for mean(T) at the level specified.
	283	<br><br>
	284
	285	</dd>
	286
	287	<script>explorer.outline.writeEnabled = true;</script>
	288	<dt><span class="decl">ConfInt
	289	<span class="currsymbol">studentsTTest</span>
	290	<script>explorer.outline.addDecl('studentsTTest');</script>
	291
	292	(T)(T <span class="funcparam">summary</span>, real <span class="funcparam">testMean</span> = 0, Alt <span class="funcparam">alt</span> = Alt.TWOSIDE, real <span class="funcparam">confLevel</span> = 0.95);
	293	</span></dt>
	294	<script>explorer.outline.writeEnabled = false;</script>
	295
	296
	297	<dd>Calculate the test directly from summary statistics of the data.
266	298	<br><br>
267	299
…	…
294	326	<script>explorer.outline.writeEnabled = true;</script>
295	327	<dt><span class="decl">ConfInt
	328	<span class="currsymbol">studentsTTest</span>
	329	<script>explorer.outline.addDecl('studentsTTest');</script>
	330
	331	(T, U)(T <span class="funcparam">sample1Summary</span>, U <span class="funcparam">sample2Summary</span>, real <span class="funcparam">testMean</span> = 0, Alt <span class="funcparam">alt</span> = Alt.TWOSIDE, real <span class="funcparam">confLevel</span> = 0.95);
	332	</span></dt>
	333	<script>explorer.outline.writeEnabled = false;</script>
	334
	335
	336	<dd>Calculate the test directly from summary statistics for each sample.
	337	<br><br>
	338
	339	</dd>
	340
	341	<script>explorer.outline.writeEnabled = true;</script>
	342	<dt><span class="decl">ConfInt
296	343	<span class="currsymbol">welchTTest</span>
297	344	<script>explorer.outline.addDecl('welchTTest');</script>
…	…
311	358	boundaries of the confidence interval for the difference between means
312	359	of sample1 and sample2 at the specified level.
	360	<br><br>
	361
	362	</dd>
	363
	364	<script>explorer.outline.writeEnabled = true;</script>
	365	<dt><span class="decl">ConfInt
	366	<span class="currsymbol">welchTTest</span>
	367	<script>explorer.outline.addDecl('welchTTest');</script>
	368
	369	(T, U)(T <span class="funcparam">sample1Summary</span>, U <span class="funcparam">sample2Summary</span>, real <span class="funcparam">testMean</span> = 0, Alt <span class="funcparam">alt</span> = Alt.TWOSIDE, real <span class="funcparam">confLevel</span> = 0.95);
	370	</span></dt>
	371	<script>explorer.outline.writeEnabled = false;</script>
	372
	373
	374	<dd>Calculate the test directly from summary statistics for each sample.
313	375	<br><br>
314	376
…	…
336	398	boundaries of the confidence interval for the mean difference between
337	399	corresponding elements of sample1 and sample2 at the specified level.
	400	<br><br>
	401
	402	</dd>
	403
	404	<script>explorer.outline.writeEnabled = true;</script>
	405	<dt><span class="decl">ConfInt
	406	<span class="currsymbol">pairedTTest</span>
	407	<script>explorer.outline.addDecl('pairedTTest');</script>
	408
	409	(T)(T <span class="funcparam">diffSummary</span>, real <span class="funcparam">testMean</span> = 0, Alt <span class="funcparam">alt</span> = Alt.TWOSIDE, real <span class="funcparam">confLevel</span> = 0.95);
	410	</span></dt>
	411	<script>explorer.outline.writeEnabled = false;</script>
	412
	413
	414	<dd>Compute the test directly from summary statistics of the differences between
	415	corresponding samples.
338	416	<br><br>
339	417
…	…
404	482	<b>References:</b><br>
405	483	"Concepts and Applications of Inferrential Statistics".
406		Richard Lowry. Vassar College. ~~Online~~ version.
	484	Richard Lowry. Vassar College. version.
407	485	<br><br>
408	486	<b>http:</b><br>
…	…
810	888
811	889	Yates's continuity correction is never used in this implementation. If
812		you want something conservative, use fisherExact().
	890	you want something that's guaranteed to be conservative, use fisherExact().
813	891	<br><br>
814	892
…	…
1049	1127	<script>explorer.outline.writeEnabled = true;</script>
1050	1128	<dt><span class="decl">struct
1051		<span class="currsymbol">~~Online~~RunsTest</span>
1052		<script>explorer.outline.addDecl('~~Online~~RunsTest');</script>
	1129	<span class="currsymbol">RunsTest</span>
	1130	<script>explorer.outline.addDecl('RunsTest');</script>
1053	1131
1054	1132	(alias positive = "a > 0",T);
…	…
1092	1170	<script>explorer.outline.writeEnabled = true;</script>
1093	1171	<dt><span class="decl">real
1094		<span class="currsymbol">p~~Val~~</span>
1095		<script>explorer.outline.addDecl('p~~Val~~');</script>
	1172	<span class="currsymbol">p</span>
	1173	<script>explorer.outline.addDecl('p');</script>
1096	1174
1097	1175	(Alt <span class="funcparam">alt</span> = Alt.TWOSIDE);
…	…
1408	1486	Page was generated with
1409	1487	<img src="candydoc/img/candydoc.gif" style="vertical-align:middle; position:relative; top:-1px">
1410		on ~~Tue Oct 13 20:16:26~~ 2009
	1488	on Sun Oct 18 13:42:21 2009
1411	1489
1412	1490	</td></tr>

trunk/alloc.d

r86	r88
3	3	* Author: David Simcha*/
4	4	/*
5		* You may use this software under your choice of either of the following
6		* licenses. YOU NEED ONLY OBEY THE TERMS OF EXACTLY ONE OF THE TWO LICENSES.
7		* IF YOU CHOOSE TO USE THE PHOBOS LICENSE, YOU DO NOT NEED TO OBEY THE TERMS OF
8		* THE BSD LICENSE. IF YOU CHOOSE TO USE THE BSD LICENSE, YOU DO NOT NEED
9		* TO OBEY THE TERMS OF THE PHOBOS LICENSE. IF YOU ARE A LAWYER LOOKING FOR
10		* LOOPHOLES AND RIDICULOUSLY NON-EXISTENT AMBIGUITIES IN THE PREVIOUS STATEMENT,
11		* GET A LIFE.
	5	* License:
	6	* Boost Software License - Version 1.0 - August 17th, 2003
12	7	*
13		* ---------------------Phobos License: ---------------------------------------
	8	* Permission is hereby granted, free of charge, to any person or organization
	9	* obtaining a copy of the software and accompanying documentation covered by
	10	* this license (the "Software") to use, reproduce, display, distribute,
	11	* execute, and transmit the Software, and to prepare derivative works of the
	12	* Software, and to permit third-parties to whom the Software is furnished to
	13	* do so, all subject to the following:
14	14	*
15		* Copyright (C) 2008-2009 by David Simcha.
	15	* The copyright notices in the Software and this entire statement, including
	16	* the above license grant, this restriction and the following disclaimer,
	17	* must be included in all copies of the Software, in whole or in part, and
	18	* all derivative works of the Software, unless such copies or derivative
	19	* works are solely in the form of machine-executable object code generated by
	20	* a source language processor.
16	21	*
17		* This software is provided 'as-is', without any express or implied
18		* warranty. In no event will the authors be held liable for any damages
19		* arising from the use of this software.
20		*
21		* Permission is granted to anyone to use this software for any purpose,
22		* including commercial applications, and to alter it and redistribute it
23		* freely, in both source and binary form, subject to the following
24		* restrictions:
25		*
26		* o The origin of this software must not be misrepresented; you must not
27		* claim that you wrote the original software. If you use this software
28		* in a product, an acknowledgment in the product documentation would be
29		* appreciated but is not required.
30		* o Altered source versions must be plainly marked as such, and must not
31		* be misrepresented as being the original software.
32		* o This notice may not be removed or altered from any source
33		* distribution.
34		*
35		* --------------------BSD License: -----------------------------------------
36		*
37		* Copyright (c) 2008-2009, David Simcha
38		* All rights reserved.
39		*
40		* Redistribution and use in source and binary forms, with or without
41		* modification, are permitted provided that the following conditions are met:
42		*
43		* * Redistributions of source code must retain the above copyright
44		* notice, this list of conditions and the following disclaimer.
45		*
46		* * Redistributions in binary form must reproduce the above copyright
47		* notice, this list of conditions and the following disclaimer in the
48		* documentation and/or other materials provided with the distribution.
49		*
50		* * Neither the name of the authors nor the
51		* names of its contributors may be used to endorse or promote products
52		* derived from this software without specific prior written permission.
53		*
54		* THIS SOFTWARE IS PROVIDED ''AS IS'' AND ANY
55		* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
56		* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
57		* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
58		* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
59		* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
60		* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
61		* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
62		* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
63		* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	22	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	23	* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	24	* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
	25	* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
	26	* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
	27	* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
	28	* DEALINGS IN THE SOFTWARE.
64	29	*/
65	30

trunk/base.d

r86	r88
6	6	* Author: David Simcha*/
7	7	/*
8		* You may use this software under your choice of either of the following
9		* licenses. YOU NEED ONLY OBEY THE TERMS OF EXACTLY ONE OF THE TWO LICENSES.
10		* IF YOU CHOOSE TO USE THE PHOBOS LICENSE, YOU DO NOT NEED TO OBEY THE TERMS OF
11		* THE BSD LICENSE. IF YOU CHOOSE TO USE THE BSD LICENSE, YOU DO NOT NEED
12		* TO OBEY THE TERMS OF THE PHOBOS LICENSE. IF YOU ARE A LAWYER LOOKING FOR
13		* LOOPHOLES AND RIDICULOUSLY NON-EXISTENT AMBIGUITIES IN THE PREVIOUS STATEMENT,
14		* GET A LIFE.
15		*
16		* ---------------------Phobos License: ---------------------------------------
17		*
18		* Copyright (C) 2008-2009 by David Simcha.
19		*
20		* This software is provided 'as-is', without any express or implied
21		* warranty. In no event will the authors be held liable for any damages
22		* arising from the use of this software.
23		*
24		* Permission is granted to anyone to use this software for any purpose,
25		* including commercial applications, and to alter it and redistribute it
26		* freely, in both source and binary form, subject to the following
27		* restrictions:
28		*
29		* o The origin of this software must not be misrepresented; you must not
30		* claim that you wrote the original software. If you use this software
31		* in a product, an acknowledgment in the product documentation would be
32		* appreciated but is not required.
33		* o Altered source versions must be plainly marked as such, and must not
34		* be misrepresented as being the original software.
35		* o This notice may not be removed or altered from any source
36		* distribution.
37		*
38		* --------------------BSD License: -----------------------------------------
39		*
40		* Copyright (c) 2008-2009, David Simcha
41		* All rights reserved.
42		*
43		* Redistribution and use in source and binary forms, with or without
44		* modification, are permitted provided that the following conditions are met:
45		*
46		* * Redistributions of source code must retain the above copyright
47		* notice, this list of conditions and the following disclaimer.
48		*
49		* * Redistributions in binary form must reproduce the above copyright
50		* notice, this list of conditions and the following disclaimer in the
51		* documentation and/or other materials provided with the distribution.
52		*
53		* * Neither the name of the authors nor the
54		* names of its contributors may be used to endorse or promote products
55		* derived from this software without specific prior written permission.
56		*
57		* THIS SOFTWARE IS PROVIDED ''AS IS'' AND ANY
58		* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
59		* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
60		* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
61		* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
62		* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
63		* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
64		* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
65		* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
66		* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	8	* License:
	9	* Boost Software License - Version 1.0 - August 17th, 2003
	10	*
	11	* Permission is hereby granted, free of charge, to any person or organization
	12	* obtaining a copy of the software and accompanying documentation covered by
	13	* this license (the "Software") to use, reproduce, display, distribute,
	14	* execute, and transmit the Software, and to prepare derivative works of the
	15	* Software, and to permit third-parties to whom the Software is furnished to
	16	* do so, all subject to the following:
	17	*
	18	* The copyright notices in the Software and this entire statement, including
	19	* the above license grant, this restriction and the following disclaimer,
	20	* must be included in all copies of the Software, in whole or in part, and
	21	* all derivative works of the Software, unless such copies or derivative
	22	* works are solely in the form of machine-executable object code generated by
	23	* a source language processor.
	24	*
	25	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	26	* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	27	* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
	28	* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
	29	* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
	30	* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
	31	* DEALINGS IN THE SOFTWARE.
67	32	*/
68
69	33	module dstats.base;
70	34
…	…
72	36	private import dstats.sort, std.c.stdlib, std.bigint, std.typecons,
73	37	std.functional, std.algorithm, std.range, std.bitmanip,
74		std.stdio;
	38	std.stdio, std.contracts;
75	39
76	40	import std.string : strip;
…	…
79	43	immutable real[] staticLogFacTable;
80	44
81		enum : size_t {
82		staticFacTableLen = 10_000,
83		}
	45	private enum size_t staticFacTableLen = 10_000;
84	46
85	47	static this() {
…	…
262	224	if(isForwardRange!(T) && realInput!(T) && isIntegral!(Ret))
263	225	in {
264		~~assert(nbin <= Ret.max + 1);~~
265	226	assert(nbin > 0);
266	227	} body {
	228	// This condition is too important, too non-obvious and too cheap to check
	229	// to be turned off in release mode:
	230	enforce(nbin <= (cast(uint) Ret.max) + 1, "Cannot bin into " ~
	231	to!string(nbin) ~ " bins and store the results in a " ~
	232	Ret.stringof ~ ".");
	233
267	234	alias ElementType!(T) E;
268	235	Unqual!(E) min = data.front, max = data.front;
…	…
306	273	assert(res == [cast(ubyte) 0, 0, 0, 0, 1, 3, 5, 7, 8, 9]);
307	274	TempAlloc.free;
	275
	276	// Make sure this throws:
	277	try {
	278	auto foo = bin( seq(0U, 1_000U), 512);
	279	assert(0);
	280	} catch(Exception e) {
	281	// It's supposed to throw.
	282	}
	283
308	284	writeln("Passed bin unittest.");
309	285	}
…	…
326	302	assert(nbin > 0);
327	303	assert(nbin <= data.length);
328		~~assert(nbin <= Ret.max + 1);~~
329	304	} body {
	305	// This condition is too important, too non-obvious and too cheap to check
	306	// to be turned off in release mode:
	307	enforce(nbin <= (cast(uint) Ret.max) + 1, "Cannot bin into " ~
	308	to!string(nbin) ~ " bins and store the results in a " ~
	309	Ret.stringof ~ ".");
	310
330	311	Ret[] result;
331	312	if(alloc == Alloc.HEAP) {
…	…
365	346	assert(res == [cast(ubyte) 1, 0, 1, 0, 2, 3, 0, 2, 2, 1, 1, 3, 3, 2, 3, 0]);
366	347	TempAlloc.free;
	348
	349	// Make sure this throws:
	350	try {
	351	auto foo = frqBin( seq(0U, 1_000U), 512);
	352	assert(0);
	353	} catch(Exception e) {
	354	// It's supposed to throw.
	355	}
	356
367	357	writeln("Passed frqBin unittest.");
368	358	}
…	…
375	365	* auto s = seq(0, 5);
376	366	* assert(s == [0, 1, 2, 3, 4]);
377		* ---*/
378
	367	* ---
	368	*/
379	369	T[] seq(T)(T start, T end, T increment = 1, Alloc alloc = Alloc.HEAP) {
380	370	T[] output;
…	…
463	453	}
464	454
465		// Used internally by rank().
	455	// Used internally by rank() and dstats.cor.scor().
466	456	void averageTies(T, U)(T sortedInput, U[] ranks, uint[] perms) nothrow
467	457	in {
…	…
538	528	///
539	529	/*Values up to 9,999 are pre-calculated and stored in
540		* an i~~nvariant~~ global array, for performance. After this point, the gamma
	530	* an immutable global array, for performance. After this point, the gamma
541	531	* function is used, because caching would take up too much memory, and if
542	532	* done lazily, would cause threading issues.*/
…	…
577	567	writefln("Passed logNcomb unit test.");
578	568	}
579
580		~~/////No, nothing this horribly inefficient is used internally.~~
581		~~//BigInt factorial(uint N) {~~
582		~~// BigInt result = 1;~~
583		~~// for(uint i = 2; i <= N; i++) {~~
584		~~// result *= i;~~
585		~~// }~~
586		~~// return result;~~
587		~~//}~~
588		//
589		~~//unittest {~~
590		~~// assert(factorial(4) == 24);~~
591		~~// assert(factorial(5) == 120);~~
592		~~// assert(factorial(6) == 720);~~
593		~~// assert(factorial(7) == 5040);~~
594		~~// assert(factorial(3) == 6);~~
595		~~// writefln("Passed factorial test.");~~
596		~~//}~~
597	569
598	570	/**A struct that generates all possible permutations of a sequence,
…	…
618	590	* assert(res.canFind([3.0, 2.0, 1.0]));
619	591	* assert(res.length == 6);
620		* ---*/
	592	* ---
	593	*/
621	594	struct Perm(T = uint) {
622	595	private:
…	…
757	730	}
758	731	writeln("Passed Perm test.");
759		}
760
761		~~private template CombRet(T) {~~
762		~~static if(isForwardRange!(T)) {~~
763		~~alias Comb!(Unqual!(ElementType!(T))) CombRet;~~
764		~~} else static if(is(T : uint)) {~~
765		~~alias Comb!uint CombRet;~~
766		~~} else static assert(0, "comb can only be created with range or uint.");~~
767		}
768
769		~~/**Create a Comb struct from a range or of a set of bounds.~~
770		*
771		* Note: CombRet is just a template to figure out what this should return.
772		* I would use auto if not for bug 2251.
773		*
774		* Examples:
775		* ---
776		* auto p = comb([1,2,3]);
777		* auto p = comb(5); // Permutations of integers on range [0, 5].
778		* ---
779		*/
780		~~CombRet!(T) comb(T)(T stuff, uint r) {~~
781		~~alias typeof(return) rt;~~
782		~~static if(isForwardRange!(T)) {~~
783		~~return rt(stuff, r);~~
784		~~} else {~~
785		~~return rt(seq(0U, cast(uint) stuff), r);~~
786		}
787	732	}
788	733
…	…
909	854	}
910	855
	856	private template CombRet(T) {
	857	static if(isForwardRange!(T)) {
	858	alias Comb!(Unqual!(ElementType!(T))) CombRet;
	859	} else static if(is(T : uint)) {
	860	alias Comb!uint CombRet;
	861	} else static assert(0, "comb can only be created with range or uint.");
	862	}
	863
	864	/**Create a Comb struct from a range or of a set of bounds.
	865	*
	866	* Note: CombRet is just a template to figure out what this should return.
	867	* I would use auto if not for bug 2251.
	868	*
	869	* Examples:
	870	* ---
	871	* auto p = comb([1,2,3]);
	872	* auto p = comb(5); // Permutations of integers on range [0, 5].
	873	* ---
	874	*/
	875	CombRet!(T) comb(T)(T stuff, uint r) {
	876	alias typeof(return) rt;
	877	static if(isForwardRange!(T)) {
	878	return rt(stuff, r);
	879	} else {
	880	return rt(seq(0U, cast(uint) stuff), r);
	881	}
	882	}
	883
911	884	unittest {
912	885	// Test indexing verison first.

trunk/cor.d

r87	r88
3	3	* Author: David Simcha*/
4	4	/*
5		* You may use this software under your choice of either of the following
6		* licenses. YOU NEED ONLY OBEY THE TERMS OF EXACTLY ONE OF THE TWO LICENSES.
7		* IF YOU CHOOSE TO USE THE PHOBOS LICENSE, YOU DO NOT NEED TO OBEY THE TERMS OF
8		* THE BSD LICENSE. IF YOU CHOOSE TO USE THE BSD LICENSE, YOU DO NOT NEED
9		* TO OBEY THE TERMS OF THE PHOBOS LICENSE. IF YOU ARE A LAWYER LOOKING FOR
10		* LOOPHOLES AND RIDICULOUSLY NON-EXISTENT AMBIGUITIES IN THE PREVIOUS STATEMENT,
11		* GET A LIFE.
12		*
13		* ---------------------Phobos License: ---------------------------------------
14		*
15		* Copyright (C) 2008-2009 by David Simcha.
16		*
17		* This software is provided 'as-is', without any express or implied
18		* warranty. In no event will the authors be held liable for any damages
19		* arising from the use of this software.
20		*
21		* Permission is granted to anyone to use this software for any purpose,
22		* including commercial applications, and to alter it and redistribute it
23		* freely, in both source and binary form, subject to the following
24		* restrictions:
25		*
26		* o The origin of this software must not be misrepresented; you must not
27		* claim that you wrote the original software. If you use this software
28		* in a product, an acknowledgment in the product documentation would be
29		* appreciated but is not required.
30		* o Altered source versions must be plainly marked as such, and must not
31		* be misrepresented as being the original software.
32		* o This notice may not be removed or altered from any source
33		* distribution.
34		*
35		* --------------------BSD License: -----------------------------------------
36		*
37		* Copyright (c) 2008-2009, David Simcha
38		* All rights reserved.
39		*
40		* Redistribution and use in source and binary forms, with or without
41		* modification, are permitted provided that the following conditions are met:
42		*
43		* * Redistributions of source code must retain the above copyright
44		* notice, this list of conditions and the following disclaimer.
45		*
46		* * Redistributions in binary form must reproduce the above copyright
47		* notice, this list of conditions and the following disclaimer in the
48		* documentation and/or other materials provided with the distribution.
49		*
50		* * Neither the name of the authors nor the
51		* names of its contributors may be used to endorse or promote products
52		* derived from this software without specific prior written permission.
53		*
54		* THIS SOFTWARE IS PROVIDED ''AS IS'' AND ANY
55		* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
56		* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
57		* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
58		* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
59		* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
60		* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
61		* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
62		* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
63		* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	5	* License:
	6	* Boost Software License - Version 1.0 - August 17th, 2003
	7	*
	8	* Permission is hereby granted, free of charge, to any person or organization
	9	* obtaining a copy of the software and accompanying documentation covered by
	10	* this license (the "Software") to use, reproduce, display, distribute,
	11	* execute, and transmit the Software, and to prepare derivative works of the
	12	* Software, and to permit third-parties to whom the Software is furnished to
	13	* do so, all subject to the following:
	14	*
	15	* The copyright notices in the Software and this entire statement, including
	16	* the above license grant, this restriction and the following disclaimer,
	17	* must be included in all copies of the Software, in whole or in part, and
	18	* all derivative works of the Software, unless such copies or derivative
	19	* works are solely in the form of machine-executable object code generated by
	20	* a source language processor.
	21	*
	22	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	23	* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	24	* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
	25	* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
	26	* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
	27	* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
	28	* DEALINGS IN THE SOFTWARE.
64	29	*/
65	30
…	…
80	45	}
81	46
82		/**Pearson correlation. When the term correlation is used unqualified, it is
	47	/**Convenience function for calculating Pearson correlation.
	48	* When the term correlation is used unqualified, it is
83	49	* usually referring to this quantity. This is a parametric correlation
84	50	* metric and should not be used with extremely ill-behaved data.
85	51	* This function works with any pair of input ranges. If they are of different
86		* lengths, it uses the first min(input1.length, input2.length) elements.*/
87		real pcor(T, U)(T input1, U input2)
	52	* lengths, it uses the first min(input1.length, input2.length) elements.
	53	*
	54	* Note: The Pcor struct returned by this function is alias this'd to the
	55	* correlation coefficient. Therefore, the result from this function can
	56	* be treated simply as a floating point number.
	57	*/
	58	Pcor pcor(T, U)(T input1, U input2)
88	59	if(realInput!(T) && realInput!(U)) {
89		~~Online~~Pcor corCalc;
	60	Pcor corCalc;
90	61	while(!input1.empty && !input2.empty) {
91	62	corCalc.put(input1.front, input2.front);
…	…
94	65	}
95	66
96		return corCalc~~.cor~~;
	67	return corCalc;
97	68	}
98	69
…	…
128	99	* Getters for stdev, var, cov, cor cost floating point division ops. Getters
129	100	* for means cost a single branch to check for N == 0. This struct uses O(1)
130		* space.*/
131		struct OnlinePcor {
	101	* space.
	102	*
	103	* Pcor.cor is alias this'd, so if this struct is used as a real, it will
	104	* be converted to a simple correlation coefficient automatically.
	105	*/
	106	struct Pcor {
132	107	private:
133	108	real _mean1 = 0, _mean2 = 0, _var1 = 0, _var2 = 0, _cov = 0, _k = 0;
134	109	public:
	110	alias cor this;
	111
135	112	///
136	113	void put(T, U)(T elem1, U elem2) {
…	…
193	170	real covariance(T, U)(T input1, U input2)
194	171	if(realInput!(T) && realInput!(U)) {
195		~~Online~~Pcor covCalc;
	172	Pcor covCalc;
196	173	while(!input1.empty && !input2.empty) {
197	174	covCalc.put(input1.front, input2.front);
…	…
259	236	averageTies(iDup2, i2Ranks, perms);
260	237
261		return pcor(i1Ranks, i2Ranks);
	238	return pcor(i1Ranks, i2Ranks).cor;
262	239	}
263	240

trunk/distrib.d

r85	r88
73	73	* because in Tango/MathExtra they represent P(X > x) while in dstats they
74	74	* represent P(X >= x).
	75	*
75	76	*
76	77	* Copyright (c) 2008-2009, David Simcha and Don Clugston
…	…
106	107	import dstats.base, std.algorithm;
107	108
108		enum SQ2PI = ~~2.5066282746310005024157652848110452530069867406099383166299L~~;
	109	enum SQ2PI = sqrt(2 * PI);
109	110
110	111	version(unittest) {
…	…
179	180	assert(stdNormal(2.5) == normalCDF(2.5, 0, 1));
180	181	}
181
182	182
183	183	///
…	…
574	574	assert(x <= n);
575	575	} body {
576		if(x > n1 \|\| x < (n - n2))
	576	if(x > n1 \|\| x < (n - n2)) {
577	577	return 0;
	578	}
578	579	real result = logNcomb(n1, x) + logNcomb(n2, n - x) - logNcomb(n1 + n2, n);
579	580	return exp(result);
…	…
652	653	assert(feqrel(chiSqrCDFR(invChiSqCDFR(3.5L, 0.1L), 3.5L), 0.1L)>=real.mant_dig-3);
653	654	assert(chiSqrCDF(0.4L, 19.02L) + chiSqrCDFR(0.4L, 19.02L) ==1.0L);
	655	assert(approxEqual( invChiSqCDFR( 3, chiSqrCDFR(1, 3)), 1));
654	656	writeln("Passed chi-square unittest.");
655	657	}
…	…
1120	1122	}
1121	1123
1122		/*
	1124	/**
1123	1125	* Inverse of complemented Fisher distribution
1124	1126	*
…	…
1425	1427
1426	1428	///
	1429	real laplacePDF(real x, real mu = 0, real b = 1) pure nothrow {
	1430	return (exp(-abs(x - mu) / b)) / (2 * b);
	1431	}
	1432
	1433	unittest {
	1434	// Values from Maxima.
	1435	assert(approxEqual(laplacePDF(3, 2, 1), 0.18393972058572));
	1436	assert(approxEqual(laplacePDF(-8, 6, 7), 0.0096668059454723));
	1437	}
	1438
	1439	///
1427	1440	real laplaceCDF(real X, real mu = 0, real b = 1) pure nothrow {
1428	1441	real diff = (X - mu);

trunk/infotheory.d

r83	r88
5	5	* Author: David Simcha*/
6	6	/*
7		* You may use this software under your choice of either of the following
8		* licenses. YOU NEED ONLY OBEY THE TERMS OF EXACTLY ONE OF THE TWO LICENSES.
9		* IF YOU CHOOSE TO USE THE PHOBOS LICENSE, YOU DO NOT NEED TO OBEY THE TERMS OF
10		* THE BSD LICENSE. IF YOU CHOOSE TO USE THE BSD LICENSE, YOU DO NOT NEED
11		* TO OBEY THE TERMS OF THE PHOBOS LICENSE. IF YOU ARE A LAWYER LOOKING FOR
12		* LOOPHOLES AND RIDICULOUSLY NON-EXISTENT AMBIGUITIES IN THE PREVIOUS STATEMENT,
13		* GET A LIFE.
14		*
15		* ---------------------Phobos License: ---------------------------------------
16		*
17		* Copyright (C) 2008-2009 by David Simcha.
18		*
19		* This software is provided 'as-is', without any express or implied
20		* warranty. In no event will the authors be held liable for any damages
21		* arising from the use of this software.
22		*
23		* Permission is granted to anyone to use this software for any purpose,
24		* including commercial applications, and to alter it and redistribute it
25		* freely, in both source and binary form, subject to the following
26		* restrictions:
27		*
28		* o The origin of this software must not be misrepresented; you must not
29		* claim that you wrote the original software. If you use this software
30		* in a product, an acknowledgment in the product documentation would be
31		* appreciated but is not required.
32		* o Altered source versions must be plainly marked as such, and must not
33		* be misrepresented as being the original software.
34		* o This notice may not be removed or altered from any source
35		* distribution.
36		*
37		* --------------------BSD License: -----------------------------------------
38		*
39		* Copyright (c) 2008-2009, David Simcha
40		* All rights reserved.
41		*
42		* Redistribution and use in source and binary forms, with or without
43		* modification, are permitted provided that the following conditions are met:
44		*
45		* * Redistributions of source code must retain the above copyright
46		* notice, this list of conditions and the following disclaimer.
47		*
48		* * Redistributions in binary form must reproduce the above copyright
49		* notice, this list of conditions and the following disclaimer in the
50		* documentation and/or other materials provided with the distribution.
51		*
52		* * Neither the name of the authors nor the
53		* names of its contributors may be used to endorse or promote products
54		* derived from this software without specific prior written permission.
55		*
56		* THIS SOFTWARE IS PROVIDED ''AS IS'' AND ANY
57		* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
58		* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
59		* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
60		* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
61		* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
62		* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
63		* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
64		* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
65		* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	7	* License:
	8	* Boost Software License - Version 1.0 - August 17th, 2003
	9	*
	10	* Permission is hereby granted, free of charge, to any person or organization
	11	* obtaining a copy of the software and accompanying documentation covered by
	12	* this license (the "Software") to use, reproduce, display, distribute,
	13	* execute, and transmit the Software, and to prepare derivative works of the
	14	* Software, and to permit third-parties to whom the Software is furnished to
	15	* do so, all subject to the following:
	16	*
	17	* The copyright notices in the Software and this entire statement, including
	18	* the above license grant, this restriction and the following disclaimer,
	19	* must be included in all copies of the Software, in whole or in part, and
	20	* all derivative works of the Software, unless such copies or derivative
	21	* works are solely in the form of machine-executable object code generated by
	22	* a source language processor.
	23	*
	24	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	25	* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	26	* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
	27	* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
	28	* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
	29	* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
	30	* DEALINGS IN THE SOFTWARE.
66	31	*/
67	32

trunk/random.d

r83	r88
1003	1003	writeln("\tMean Expected: ", a / (a + b), " Observed: ", summ.mean);
1004	1004	writeln("\tMedian Expected: ?? Observed: ", median(observ));
1005		writeln("\tStdev Expected: ", betaStdev(a, b), " Observed: ", summ.SD);
	1005	writeln("\tStdev Expected: ", betaStdev(a, b), " Observed: ", summ.stdev);
1006	1006	writeln("\tKurtosis Expected: ", betaKurtosis(a, b), " Observed: ", summ.kurtosis);
1007		writeln("\tSkewness Expected: ", betaSkew(a, b), " Observed: ", summ.skew);
	1007	writeln("\tSkewness Expected: ", betaSkew(a, b), " Observed: ", summ.skewness);
1008	1008	delete observ;
1009	1009	}

trunk/regress.d

r75	r88
6	6	*
7	7	* Author: David Simcha*/
8		/*
9		* You may use this software under your choice of either of the following
10		* licenses. YOU NEED ONLY OBEY THE TERMS OF EXACTLY ONE OF THE TWO LICENSES.
11		* IF YOU CHOOSE TO USE THE PHOBOS LICENSE, YOU DO NOT NEED TO OBEY THE TERMS OF
12		* THE BSD LICENSE. IF YOU CHOOSE TO USE THE BSD LICENSE, YOU DO NOT NEED
13		* TO OBEY THE TERMS OF THE PHOBOS LICENSE. IF YOU ARE A LAWYER LOOKING FOR
14		* LOOPHOLES AND RIDICULOUSLY NON-EXISTENT AMBIGUITIES IN THE PREVIOUS STATEMENT,
15		* GET A LIFE.
16		*
17		* ---------------------Phobos License: ---------------------------------------
18		*
19		* Copyright (C) 2009 by David Simcha.
20		*
21		* This software is provided 'as-is', without any express or implied
22		* warranty. In no event will the authors be held liable for any damages
23		* arising from the use of this software.
24		*
25		* Permission is granted to anyone to use this software for any purpose,
26		* including commercial applications, and to alter it and redistribute it
27		* freely, in both source and binary form, subject to the following
28		* restrictions:
29		*
30		* o The origin of this software must not be misrepresented; you must not
31		* claim that you wrote the original software. If you use this software
32		* in a product, an acknowledgment in the product documentation would be
33		* appreciated but is not required.
34		* o Altered source versions must be plainly marked as such, and must not
35		* be misrepresented as being the original software.
36		* o This notice may not be removed or altered from any source
37		* distribution.
38		*
39		* --------------------BSD License: -----------------------------------------
40		*
41		* Copyright (c) 2009, David Simcha
42		* All rights reserved.
43		*
44		* Redistribution and use in source and binary forms, with or without
45		* modification, are permitted provided that the following conditions are met:
46		*
47		* * Redistributions of source code must retain the above copyright
48		* notice, this list of conditions and the following disclaimer.
49		*
50		* * Redistributions in binary form must reproduce the above copyright
51		* notice, this list of conditions and the following disclaimer in the
52		* documentation and/or other materials provided with the distribution.
53		*
54		* * Neither the name of the authors nor the
55		* names of its contributors may be used to endorse or promote products
56		* derived from this software without specific prior written permission.
57		*
58		* THIS SOFTWARE IS PROVIDED ''AS IS'' AND ANY
59		* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
60		* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
61		* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
62		* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
63		* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
64		* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
65		* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
66		* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
67		* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	8	/*
	9	* License:
	10	* Boost Software License - Version 1.0 - August 17th, 2003
	11	*
	12	* Permission is hereby granted, free of charge, to any person or organization
	13	* obtaining a copy of the software and accompanying documentation covered by
	14	* this license (the "Software") to use, reproduce, display, distribute,
	15	* execute, and transmit the Software, and to prepare derivative works of the
	16	* Software, and to permit third-parties to whom the Software is furnished to
	17	* do so, all subject to the following:
	18	*
	19	* The copyright notices in the Software and this entire statement, including
	20	* the above license grant, this restriction and the following disclaimer,
	21	* must be included in all copies of the Software, in whole or in part, and
	22	* all derivative works of the Software, unless such copies or derivative
	23	* works are solely in the form of machine-executable object code generated by
	24	* a source language processor.
	25	*
	26	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	27	* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	28	* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
	29	* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
	30	* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
	31	* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
	32	* DEALINGS IN THE SOFTWARE.
68	33	*/
69	34
…	…
175	140	foreach(i, row; mat) {
176	141	real absMax = 1.0L / reduce!(max)(map!(abs)(row[0..mat.length]));
177		// row[0..mat.length] *= absMax; // Bug 3006
178		foreach(ref elem; row[0..mat.length]) {
179		elem *= absMax;
180		}
	142	row[0..mat.length] *= absMax;
181	143	row[i + mat.length] = absMax;
182	144	}
…	…
207	169	foreach(i; 0..mat.length) {
208	170	real diagVal = mat[i][i];
209		//mat[i][] /= diagVal; // Bug 3006
210		foreach(ref elem; mat[i]) {
211		elem /= diagVal;
212		}
	171	mat[i][] /= diagVal;
213	172	}
214	173
…	…
466	425	real S = 0;
467	426	uint n = 0;
468		~~Online~~Pcor R2Calc;
	427	Pcor R2Calc;
469	428	for(; !residuals.empty; residuals.popFront) {
470	429	real residual = residuals.front;

trunk/sort.d

r83	r88
31	31	* Author: David Simcha*/
32	32	/*
33		* You may use this software under your choice of either of the following
34		* licenses. YOU NEED ONLY OBEY THE TERMS OF EXACTLY ONE OF THE TWO LICENSES.
35		* IF YOU CHOOSE TO USE THE PHOBOS LICENSE, YOU DO NOT NEED TO OBEY THE TERMS OF
36		* THE BSD LICENSE. IF YOU CHOOSE TO USE THE BSD LICENSE, YOU DO NOT NEED
37		* TO OBEY THE TERMS OF THE PHOBOS LICENSE. IF YOU ARE A LAWYER LOOKING FOR
38		* LOOPHOLES AND RIDICULOUSLY NON-EXISTENT AMBIGUITIES IN THE PREVIOUS STATEMENT,
39		* GET A LIFE.
40		*
41		* ---------------------Phobos License: ---------------------------------------
42		*
43		* Copyright (C) 2008-2009 by David Simcha.
44		*
45		* This software is provided 'as-is', without any express or implied
46		* warranty. In no event will the authors be held liable for any damages
47		* arising from the use of this software.
48		*
49		* Permission is granted to anyone to use this software for any purpose,
50		* including commercial applications, and to alter it and redistribute it
51		* freely, in both source and binary form, subject to the following
52		* restrictions:
53		*
54		* o The origin of this software must not be misrepresented; you must not
55		* claim that you wrote the original software. If you use this software
56		* in a product, an acknowledgment in the product documentation would be
57		* appreciated but is not required.
58		* o Altered source versions must be plainly marked as such, and must not
59		* be misrepresented as being the original software.
60		* o This notice may not be removed or altered from any source
61		* distribution.
62		*
63		* --------------------BSD License: -----------------------------------------
64		*
65		* Copyright (c) 2008-2009, David Simcha
66		* All rights reserved.
67		*
68		* Redistribution and use in source and binary forms, with or without
69		* modification, are permitted provided that the following conditions are met:
70		*
71		* * Redistributions of source code must retain the above copyright
72		* notice, this list of conditions and the following disclaimer.
73		*
74		* * Redistributions in binary form must reproduce the above copyright
75		* notice, this list of conditions and the following disclaimer in the
76		* documentation and/or other materials provided with the distribution.
77		*
78		* * Neither the name of the authors nor the
79		* names of its contributors may be used to endorse or promote products
80		* derived from this software without specific prior written permission.
81		*
82		* THIS SOFTWARE IS PROVIDED ''AS IS'' AND ANY
83		* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
84		* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
85		* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
86		* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
87		* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
88		* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
89		* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
90		* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
91		* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	33	* License:
	34	* Boost Software License - Version 1.0 - August 17th, 2003
	35	*
	36	* Permission is hereby granted, free of charge, to any person or organization
	37	* obtaining a copy of the software and accompanying documentation covered by
	38	* this license (the "Software") to use, reproduce, display, distribute,
	39	* execute, and transmit the Software, and to prepare derivative works of the
	40	* Software, and to permit third-parties to whom the Software is furnished to
	41	* do so, all subject to the following:
	42	*
	43	* The copyright notices in the Software and this entire statement, including
	44	* the above license grant, this restriction and the following disclaimer,
	45	* must be included in all copies of the Software, in whole or in part, and
	46	* all derivative works of the Software, unless such copies or derivative
	47	* works are solely in the form of machine-executable object code generated by
	48	* a source language processor.
	49	*
	50	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	51	* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	52	* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
	53	* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
	54	* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
	55	* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
	56	* DEALINGS IN THE SOFTWARE.
92	57	*/
93	58

trunk/stats.d

r70	r88
1	1	/*Convenience module that simply publicly imports everything else./
	2	/*
	3	* License:
	4	* If you think this module is even copyrightable, you have issues.
	5	*/
2	6
3	7	module dstats.stats;

trunk/summary.d

r87	r88
12	12	* Author: David Simcha*/
13	13	/*
14		* You may use this software under your choice of either of the following
15		* licenses. YOU NEED ONLY OBEY THE TERMS OF EXACTLY ONE OF THE TWO LICENSES.
16		* IF YOU CHOOSE TO USE THE PHOBOS LICENSE, YOU DO NOT NEED TO OBEY THE TERMS OF
17		* THE BSD LICENSE. IF YOU CHOOSE TO USE THE BSD LICENSE, YOU DO NOT NEED
18		* TO OBEY THE TERMS OF THE PHOBOS LICENSE. IF YOU ARE A LAWYER LOOKING FOR
19		* LOOPHOLES AND RIDICULOUSLY NON-EXISTENT AMBIGUITIES IN THE PREVIOUS STATEMENT,
20		* GET A LIFE.
21		*
22		* ---------------------Phobos License: ---------------------------------------
23		*
24		* Copyright (C) 2008-2009 by David Simcha.
25		*
26		* This software is provided 'as-is', without any express or implied
27		* warranty. In no event will the authors be held liable for any damages
28		* arising from the use of this software.
29		*
30		* Permission is granted to anyone to use this software for any purpose,
31		* including commercial applications, and to alter it and redistribute it
32		* freely, in both source and binary form, subject to the following
33		* restrictions:
34		*
35		* o The origin of this software must not be misrepresented; you must not
36		* claim that you wrote the original software. If you use this software
37		* in a product, an acknowledgment in the product documentation would be
38		* appreciated but is not required.
39		* o Altered source versions must be plainly marked as such, and must not
40		* be misrepresented as being the original software.
41		* o This notice may not be removed or altered from any source
42		* distribution.
43		*
44		* --------------------BSD License: -----------------------------------------
45		*
46		* Copyright (c) 2008-2009, David Simcha
47		* All rights reserved.
48		*
49		* Redistribution and use in source and binary forms, with or without
50		* modification, are permitted provided that the following conditions are met:
51		*
52		* * Redistributions of source code must retain the above copyright
53		* notice, this list of conditions and the following disclaimer.
54		*
55		* * Redistributions in binary form must reproduce the above copyright
56		* notice, this list of conditions and the following disclaimer in the
57		* documentation and/or other materials provided with the distribution.
58		*
59		* * Neither the name of the authors nor the
60		* names of its contributors may be used to endorse or promote products
61		* derived from this software without specific prior written permission.
62		*
63		* THIS SOFTWARE IS PROVIDED ''AS IS'' AND ANY
64		* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
65		* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
66		* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
67		* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
68		* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
69		* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
70		* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
71		* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
72		* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	14	* License:
	15	* Boost Software License - Version 1.0 - August 17th, 2003
	16	*
	17	* Permission is hereby granted, free of charge, to any person or organization
	18	* obtaining a copy of the software and accompanying documentation covered by
	19	* this license (the "Software") to use, reproduce, display, distribute,
	20	* execute, and transmit the Software, and to prepare derivative works of the
	21	* Software, and to permit third-parties to whom the Software is furnished to
	22	* do so, all subject to the following:
	23	*
	24	* The copyright notices in the Software and this entire statement, including
	25	* the above license grant, this restriction and the following disclaimer,
	26	* must be included in all copies of the Software, in whole or in part, and
	27	* all derivative works of the Software, unless such copies or derivative
	28	* works are solely in the form of machine-executable object code generated by
	29	* a source language processor.
	30	*
	31	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	32	* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	33	* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
	34	* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
	35	* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
	36	* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
	37	* DEALINGS IN THE SOFTWARE.
73	38	*/
74	39
…	…
226	191	real mean(T)(T data)
227	192	if(realIterable!(T)) {
228		~~Online~~Mean meanCalc;
	193	Mean meanCalc;
229	194	foreach(element; data) {
230	195	meanCalc.put(element);
…	…
239	204	* Examples:
240	205	* ---
241		* ~~Online~~Mean summ;
	206	* Mean summ;
242	207	* summ.put(1);
243	208	* summ.put(2);
…	…
247	212	* assert(summ.mean == 3);
248	213	* ---*/
249		struct ~~Online~~Mean {
	214	struct Mean {
250	215	private:
251	216	real result = 0;
…	…
277	242
278	243	///
279		struct ~~Online~~GeometricMean {
	244	struct GeometricMean {
280	245	private:
281		~~Online~~Mean m;
	246	Mean m;
282	247	public:
283	248	///Allow implicit casting to real, by returning current geometric mean.
…	…
305	270	}
306	271
307
308
309	272	///
310	273	real geometricMean(T)(T data)
311	274	if(realIterable!(T)) {
312		~~Online~~GeometricMean m;
	275	GeometricMean m;
313	276	foreach(elem; data) {
314	277	m.put(elem);
…	…
353	316	* for stdev, var cost a few floating point ops. Getter for mean costs
354	317	* a single branch to check for N == 0. Relatively expensive floating point
355		* ops, if you only need mean, try ~~Online~~Mean. This struct uses O(1) space and
	318	* ops, if you only need mean, try Mean. This struct uses O(1) space and
356	319	* does NOT store the individual elements.
357	320	*
358	321	* Examples:
359	322	* ---
360		* ~~Online~~MeanSD summ;
	323	* MeanSD summ;
361	324	* summ.put(1);
362	325	* summ.put(2);
…	…
368	331	* assert(summ.var == 2.5);
369	332	* ---*/
370		struct ~~Online~~MeanSD {
	333	struct MeanSD {
371	334	private:
372	335	real _mean = 0;
…	…
396	359	}
397	360
	361	// Undocumented on purpose b/c it's for internal use only.
398	362	real mse() const {
399	363	return (_k < 2) ? real.nan : (_var - _mean * _mean);
…	…
407	371	///
408	372	string toString() {
409		return ~~forma~~t("N = ", cast(ulong) _k, "\nMean = ", mean, "\nVariance = ",
	373	return text("N = ", cast(ulong) _k, "\nMean = ", mean, "\nVariance = ",
410	374	var, "\nStdev = ", stdev);
411	375	}
412	376	}
413	377
414		/**Simple holder for mean, stdev/variance. Plain old data, accessing is
415		* cheap.*/
416		struct MeanSD {
417		///
418		real mean;
419		///
420		real SD;
421
422		string toString() {
423		return format("Mean = ", mean, "\nStdev = ", SD);
424		}
	378	/**Convenience function that puts all elements of data into a MeanSD struct,
	379	* then returns this struct.*/
	380	MeanSD meanStdev(T)(T data)
	381	if(realIterable!(T)) {
	382	MeanSD ret;
	383	foreach(elem; data) {
	384	ret.put(elem);
	385	}
	386	return ret;
425	387	}
426	388
…	…
429	391	real variance(T)(T data)
430	392	if(realIterable!(T)) {
431		return meanVariance(data).SD;
432		}
433
434		/**Calculates both mean and variance of an input range, returns a MeanSD
435		* struct.*/
436		MeanSD meanVariance(T)(T data)
437		if(realIterable!(T)) {
438		OnlineMeanSD meanSDCalc;
439		foreach(element; data) {
440		meanSDCalc.put(element);
441		}
442
443		return MeanSD(meanSDCalc.mean, meanSDCalc.var);
444		}
445
446		/**Calculates both mean and standard deviation of an input range, returns a
447		* MeanSD struct.*/
448		MeanSD meanStdev(T)(T data)
449		if(realIterable!(T)) {
450		auto ret = meanVariance(data);
451		ret.SD = sqrt(ret.SD);
452		return ret;
	393	return meanStdev(data).var;
453	394	}
454	395
…	…
457	398	real stdev(T)(T data)
458	399	if(realIterable!(T)) {
459		return meanStdev(data).SD;
	400	return meanStdev(data).stdev;
460	401	}
461	402
462	403	unittest {
463	404	auto res = meanStdev(cast(int[]) [3, 1, 4, 5]);
464		assert(approxEqual(res.SD, 1.7078));
	405	assert(approxEqual(res.stdev, 1.7078));
465	406	assert(approxEqual(res.mean, 3.25));
466	407	res = meanStdev(cast(double[]) [1.0, 2.0, 3.0, 4.0, 5.0]);
467		assert(approxEqual(res.SD, 1.5811));
	408	assert(approxEqual(res.stdev, 1.5811));
468	409	assert(approxEqual(res.mean, 3));
469	410	writefln("Passed variance/standard deviation unittest.");
…	…
472	413	/**Output range to compute mean, stdev, variance, skewness, kurtosis, min, and
473	414	* max online. Using this struct is relatively expensive, so if you just need
474		* mean and/or stdev, try ~~OnlineMeanSD or Online~~Mean. Getter methods for stdev,
	415	* mean and/or stdev, try MeanSD or Mean. Getter methods for stdev,
475	416	* var cost a few floating point ops. Getter for mean costs a single branch to
476	417	* check for N == 0. Getters for skewness and kurtosis cost a whole bunch of
…	…
480	421	* Examples:
481	422	* ---
482		* ~~Online~~Summary summ;
	423	* Summary summ;
483	424	* summ.put(1);
484	425	* summ.put(2);
…	…
494	435	* assert(summ.max == 5);
495	436	* ---*/
496		struct ~~Online~~Summary {
	437	struct Summary {
497	438	private:
498	439	real _mean = 0;
…	…
563	504	///
564	505	string toString() {
565		return ~~forma~~t("N = ", cast(ulong) _k, "\nMean = ", mean, "\nVariance = ",
	506	return text("N = ", cast(ulong) _k, "\nMean = ", mean, "\nVariance = ",
566	507	var, "\nStdev = ", stdev, "\nSkewness = ", skewness,
567	508	"\nKurtosis = ", kurtosis, "\nMin = ", _min, "\nMax = ", _max);
…	…
576	517	real kurtosis(T)(T data)
577	518	if(realIterable!(T)) {
578		~~Online~~Summary kCalc;
	519	Summary kCalc;
579	520	foreach(elem; data) {
580	521	kCalc.put(elem);
…	…
598	539	real skewness(T)(T data)
599	540	if(realIterable!(T)) {
600		~~Online~~Summary sCalc;
	541	Summary sCalc;
601	542	foreach(elem; data) {
602	543	sCalc.put(elem);
…	…
618	559	}
619	560
620		/**Plain old data struct for holding results of summary(). Accessing members
621		* is cheap.*/
622		struct Summary {
623		///
624		ulong N;
625
626		///
627		real mean;
628
629		///
630		real var;
631
632		///
633		real SD;
634
635		///
636		real skew;
637
638		///
639		real kurtosis;
640
641		///
642		real min;
643
644		///
645		real max;
646
647		///
648		string toString() {
649		return format("N = ", N, "\nMean = ", mean, "\nVariance = ",
650		var, "\nStdev = ", SD, "\nSkewness = ", skew,
651		"\nKurtosis = ", kurtosis, "\nMin = ", min, "\nMax = ", max);
652		}
653		}
654
655		/**Calculates all summary stats (mean, variance, standard dev., skewness
656		* and kurtosis) on an input range with elements that can be implicitly
657		* converted to real. Returns the results in a Summary struct.*/
	561	/**Convenience function. Puts all elements of data into a Summary struct,
	562	* and returns this struct.*/
658	563	Summary summary(T)(T data)
659	564	if(realIterable!(T)) {
660		~~Online~~Summary summ;
	565	Summary summ;
661	566	foreach(elem; data) {
662	567	summ.put(elem);
663	568	}
664		real variance = summ.var;
665		return Summary(lrint(summ.N), summ.mean, variance, sqrt(variance),
666		summ.skewness, summ.kurtosis, summ.min, summ.max);
	569	return summ;
667	570	}
668	571	// Just a convenience function for a well-tested struct. No unittest really
…	…
685	588	auto msd = meanStdev(range);
686	589	this.mean = msd.mean;
687		this.sdNeg1 = 1.0L / msd.SD;
	590	this.sdNeg1 = 1.0L / msd.stdev;
688	591	}
689	592

trunk/tests.d

r84	r88
4	4	* Author: David Simcha*/
5	5	/*
6		* You may use this software under your choice of either of the following
7		* licenses. YOU NEED ONLY OBEY THE TERMS OF EXACTLY ONE OF THE TWO LICENSES.
8		* IF YOU CHOOSE TO USE THE PHOBOS LICENSE, YOU DO NOT NEED TO OBEY THE TERMS OF
9		* THE BSD LICENSE. IF YOU CHOOSE TO USE THE BSD LICENSE, YOU DO NOT NEED
10		* TO OBEY THE TERMS OF THE PHOBOS LICENSE. IF YOU ARE A LAWYER LOOKING FOR
11		* LOOPHOLES AND RIDICULOUSLY NON-EXISTENT AMBIGUITIES IN THE PREVIOUS STATEMENT,
12		* GET A LIFE.
13		*
14		* ---------------------Phobos License: ---------------------------------------
15		*
16		* Copyright (C) 2008-2009 by David Simcha.
17		*
18		* This software is provided 'as-is', without any express or implied
19		* warranty. In no event will the authors be held liable for any damages
20		* arising from the use of this software.
21		*
22		* Permission is granted to anyone to use this software for any purpose,
23		* including commercial applications, and to alter it and redistribute it
24		* freely, in both source and binary form, subject to the following
25		* restrictions:
26		*
27		* o The origin of this software must not be misrepresented; you must not
28		* claim that you wrote the original software. If you use this software
29		* in a product, an acknowledgment in the product documentation would be
30		* appreciated but is not required.
31		* o Altered source versions must be plainly marked as such, and must not
32		* be misrepresented as being the original software.
33		* o This notice may not be removed or altered from any source
34		* distribution.
35		*
36		* --------------------BSD License: -----------------------------------------
37		*
38		* Copyright (c) 2008-2009, David Simcha
39		* All rights reserved.
40		*
41		* Redistribution and use in source and binary forms, with or without
42		* modification, are permitted provided that the following conditions are met:
43		*
44		* * Redistributions of source code must retain the above copyright
45		* notice, this list of conditions and the following disclaimer.
46		*
47		* * Redistributions in binary form must reproduce the above copyright
48		* notice, this list of conditions and the following disclaimer in the
49		* documentation and/or other materials provided with the distribution.
50		*
51		* * Neither the name of the authors nor the
52		* names of its contributors may be used to endorse or promote products
53		* derived from this software without specific prior written permission.
54		*
55		* THIS SOFTWARE IS PROVIDED ''AS IS'' AND ANY
56		* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
57		* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
58		* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
59		* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
60		* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
61		* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
62		* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
63		* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
64		* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	6	* License:
	7	* Boost Software License - Version 1.0 - August 17th, 2003
	8	*
	9	* Permission is hereby granted, free of charge, to any person or organization
	10	* obtaining a copy of the software and accompanying documentation covered by
	11	* this license (the "Software") to use, reproduce, display, distribute,
	12	* execute, and transmit the Software, and to prepare derivative works of the
	13	* Software, and to permit third-parties to whom the Software is furnished to
	14	* do so, all subject to the following:
	15	*
	16	* The copyright notices in the Software and this entire statement, including
	17	* the above license grant, this restriction and the following disclaimer,
	18	* must be included in all copies of the Software, in whole or in part, and
	19	* all derivative works of the Software, unless such copies or derivative
	20	* works are solely in the form of machine-executable object code generated by
	21	* a source language processor.
	22	*
	23	* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	24	* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	25	* FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
	26	* SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
	27	* FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
	28	* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
	29	* DEALINGS IN THE SOFTWARE.
65	30	*/
66	31	module dstats.tests;
67	32
68	33	import dstats.base, dstats.distrib, dstats.alloc, dstats.summary, dstats.sort,
69		dstats.cor, std.algorithm, std.functional, std.range, std.c.stdlib,
70		std.conv;
	34	dstats.cor, std.algorithm, std.functional, std.range, std.conv;
71	35
72	36	version(unittest) {
73	37	import std.stdio, dstats.random;
74
75		~~Random gen;~~
76
77		~~static this() {~~
78		~~gen.seed(unpredictableSeed);~~
79		}
80
81	38	void main(){}
82	39	}
…	…
140	97	}
141	98
	99	/**Tests whether a struct/class has the necessary information for calculating
	100	* a T-test. It must have a property .mean (mean), .stdev (stdandard deviation),
	101	* .var (variance), and .N (sample size).
	102	*/
	103	template isSummary(T) {
	104	enum bool isSummary = is(typeof(T.init.mean)) && is(typeof(T.init.stdev)) &&
	105	is(typeof(T.init.var)) && is(typeof(T.init.N));
	106	}
	107
142	108	/**One-sample Student's T-test for difference between mean of data and
143	109	* a fixed value. Alternatives are Alt.LESS, meaning mean(data) < testMean,
…	…
150	116	real confLevel = 0.95)
151	117	if(realIterable!(T)) {
152		return pairedTTest(data, repeat(0), testMean, alt, confLevel);
153
	118	return studentsTTest( meanStdev(data), testMean, alt, confLevel);
	119
	120	}
	121
	122	/*Calculate the test directly from summary statistics of the data./
	123	ConfInt studentsTTest(T)(T summary, real testMean = 0, Alt alt = Alt.TWOSIDE,
	124	real confLevel = 0.95)
	125	if(isSummary!T) {
	126	return pairedTTest(summary, testMean, alt, confLevel);
154	127	}
155	128
…	…
188	161	Alt alt = Alt.TWOSIDE, real confLevel = 0.95)
189	162	if(realIterable!(T) && realIterable!(U)) {
190		size_t n1, n2;
191		OnlineMeanSD s1summ, s2summ;
192		foreach(elem; sample1) {
193		s1summ.put(elem);
194		n1++;
195		}
196		foreach(elem; sample2) {
197		s2summ.put(elem);
198		n2++;
199		}
	163	return studentsTTest( meanStdev(sample1), meanStdev(sample2),
	164	testMean, alt, confLevel);
	165	}
	166
	167	/*Calculate the test directly from summary statistics for each sample./
	168	ConfInt studentsTTest(T, U)(T sample1Summary, U sample2Summary,
	169	real testMean = 0, Alt alt = Alt.TWOSIDE, real confLevel = 0.95)
	170	if(isSummary!T && isSummary!U) {
	171	// Save some typing.
	172	alias sample1Summary s1summ;
	173	alias sample2Summary s2summ;
	174
	175	real n1 = s1summ.N,
	176	n2 = s2summ.N;
200	177
201	178	real sx1x2 = sqrt(((n1 - 1) * s1summ.var + (n2 - 1) * s2summ.var) /
…	…
272	249	Alt alt = Alt.TWOSIDE, real confLevel = 0.95)
273	250	if(realIterable!(T) && realIterable!(U)) {
274		size_t n1, n2;
275		OnlineMeanSD s1summ, s2summ;
276		foreach(elem; sample1) {
277		s1summ.put(elem);
278		n1++;
279		}
280		foreach(elem; sample2) {
281		s2summ.put(elem);
282		n2++;
283		}
	251	return welchTTest( meanStdev(sample1), meanStdev(sample2),
	252	testMean, alt, confLevel);
	253	}
	254
	255	/*Calculate the test directly from summary statistics for each sample./
	256	ConfInt welchTTest(T, U)(T sample1Summary, U sample2Summary, real testMean = 0,
	257	Alt alt = Alt.TWOSIDE, real confLevel = 0.95)
	258	if(isSummary!(T) && isSummary!(U)) {
	259	// Save typing.
	260	alias sample1Summary s1summ;
	261	alias sample2Summary s2summ;
	262
	263	real n1 = s1summ.N,
	264	n2 = s2summ.N;
284	265
285	266	auto v1 = s1summ.var, v2 = s2summ.var;
…	…
358	339	Alt alt = Alt.TWOSIDE, real confLevel = 0.95)
359	340	if(realInput!(T) && realInput!(U)) {
360		OnlineMeanSD msd;
361		size_t len = 0;
	341	MeanSD msd;
362	342	while(!before.empty && !after.empty) {
363	343	real diff = cast(real) before.front - cast(real) after.front;
…	…
365	345	after.popFront;
366	346	msd.put(diff);
367		len++;
368		}
	347	}
	348
	349	return pairedTTest(msd, testMean, alt, confLevel);
	350	}
	351
	352	/**Compute the test directly from summary statistics of the differences between
	353	* corresponding samples.*/
	354	ConfInt pairedTTest(T)(T diffSummary, real testMean = 0,
	355	Alt alt = Alt.TWOSIDE, real confLevel = 0.95)
	356	if(isSummary!T) {
	357	// Save typing.
	358	alias diffSummary msd;
369	359
370	360	ConfInt ret;
371		ret.testStat = (msd.mean - testMean) / msd.stdev * sqrt(~~cast(real) len~~);
	361	ret.testStat = (msd.mean - testMean) / msd.stdev * sqrt(msd.N);
372	362	auto sampleMean = msd.mean;
373	363	auto sampleSd = msd.stdev;
374		real normSd = sampleSd / sqrt(~~cast(real) len~~);
	364	real normSd = sampleSd / sqrt(msd.N);
375	365	ret.testStat = (sampleMean - testMean) / normSd;
376	366
…	…
378	368	return ret;
379	369	} else if(alt == Alt.LESS) {
380		ret.p = studentsTCDF(ret.testStat, ~~len~~ - 1);
381		real delta = invStudentsTCDF(1 - confLevel, ~~len~~ - 1) * normSd;
	370	ret.p = studentsTCDF(ret.testStat, msd.N - 1);
	371	real delta = invStudentsTCDF(1 - confLevel, msd.N - 1) * normSd;
382	372	ret.lowerBound = -real.infinity;
383	373	ret.upperBound = sampleMean - delta;
384	374	} else if(alt == Alt.GREATER) {
385		ret.p = studentsTCDF(-ret.testStat, ~~len~~ - 1);
386		real delta = invStudentsTCDF(1 - confLevel, ~~len~~ - 1) * normSd;
	375	ret.p = studentsTCDF(-ret.testStat, msd.N - 1);
	376	real delta = invStudentsTCDF(1 - confLevel, msd.N - 1) * normSd;
387	377	ret.lowerBound = sampleMean + delta;
388	378	ret.upperBound = real.infinity;
389	379	} else {
390		ret.p = 2 * min(studentsTCDF(ret.testStat, ~~len~~ - 1),
391		studentsTCDF(-ret.testStat, ~~len~~ - 1));
392		real delta = invStudentsTCDF(0.5 * (1 - confLevel), ~~len~~ - 1) * normSd;
	380	ret.p = 2 * min(studentsTCDF(ret.testStat, msd.N - 1),
	381	studentsTCDF(-ret.testStat, msd.N - 1));
	382	real delta = invStudentsTCDF(0.5 * (1 - confLevel), msd.N - 1) * normSd;
393	383	ret.lowerBound = sampleMean + delta;
394	384	ret.upperBound = sampleMean - delta;
…	…
429	419	mixin(newFrame);
430	420	auto data = tempdup(dataIn[0]);
431		auto withins = newStack!~~Online~~MeanSD(data.length);
432		withins[] = ~~Online~~MeanSD.init;
	421	auto withins = newStack!MeanSD(data.length);
	422	withins[] = MeanSD.init;
433	423	} else {
434	424	enum len = dataIn.length;
435	425	alias dataIn data;
436		~~Online~~MeanSD[len] withins;
437		}
438
439		~~Online~~Mean overallMean;
	426	MeanSD[len] withins;
	427	}
	428
	429	Mean overallMean;
440	430	uint DFGroups = data.length - 1;
441	431	uint DFDataPoints = 0;
…	…
510	500	*
511	501	* References: "Concepts and Applications of Inferrential Statistics".
512		* Richard Lowry. Vassar College. ~~Online~~ version.
	502	* Richard Lowry. Vassar College. version.
513	503	* http://faculty.vassar.edu/lowry/webtext.html
514	504	*/
…	…
518	508	mixin(newFrame);
519	509	auto data = tempdup(dataIn[0]);
520		auto withins = newStack!~~Online~~MeanSD(data.length);
521		withins[] = ~~Online~~MeanSD.init;
	510	auto withins = newStack!MeanSD(data.length);
	511	withins[] = MeanSD.init;
522	512	} else {
523	513	enum len = dataIn.length;
524	514	alias dataIn data;
525		~~Online~~MeanSD[len] withins;
526		}
527		~~Online~~MeanSD overallSumm;
	515	MeanSD[len] withins;
	516	}
	517	MeanSD overallSumm;
528	518	real nGroupNeg1 = 1.0L / data.length;
529	519
…	…
618	608	mixin(newFrame);
619	609	size_t N = 0;
	610
620	611	static if(dataIn.length == 1 && isInputRange!(typeof(dataIn[0].front))) {
621	612	auto data = tempdup(dataIn[0]);
…	…
671	662	real rBar = 0.5L * (N + 1);
672	663	foreach(meanI, l; lengths) {
673		~~Online~~Mean groupStats;
	664	Mean groupStats;
674	665	foreach(i; index..index + l) {
675	666	groupStats.put( ranks[i]);
…	…
749	740	auto ranks = newStack!float(data.length);
750	741	auto dataPoints = newStack!real(data.length);
751		auto colMeans = newStack!~~Online~~Mean(data.length);
752		colMeans[] = ~~Online~~Mean.init;
	742	auto colMeans = newStack!Mean(data.length);
	743	colMeans[] = Mean.init;
753	744	} else {
754	745	enum len = dataIn.length;
…	…
756	747	float[len] ranks;
757	748	real[len] dataPoints;
758		~~Online~~Mean[len] colMeans;
	749	Mean[len] colMeans;
759	750	}
760	751	real rBar = cast(real) data.length * (data.length + 1.0L) / 2.0L;
761		~~Online~~MeanSD overallSumm;
	752	MeanSD overallSumm;
762	753
763	754	bool someEmpty() {
…	…
917	908	}
918	909
919		real wilcoxonRankSumW(T)(T sample1, T sample2, real* tieSum = null)
	910	private real wilcoxonRankSumW(T)(T sample1, T sample2, real* tieSum = null)
920	911	if(isInputRange!(T) && dstats.base.hasLength!(T)) {
921	912	uint n1 = sample1.length, n2 = sample2.length, N = n1 + n2;
…	…
954	945	}
955	946
	947	private
956	948	real wilcoxonRankSumPval(T)(T w, ulong n1, ulong n2, Alt alt = Alt.TWOSIDE,
957	949	real tieSum = 0, uint exactThresh = 50) {
	950	if(alt == Alt.NONE) {
	951	return real.nan;
	952	}
	953
958	954	ulong N = n1 + n2;
959	955
…	…
990	986	* programming to count the number of combinations of numbers [1..N] that sum
991	987	* of length n1 that sum to <= W in O(N * W * n1) time.*/
992		real wilcoxRSPExact(uint W, uint n1, uint n2, Alt alt = Alt.TWOSIDE) {
	988	private real wilcoxRSPExact(uint W, uint n1, uint n2, Alt alt = Alt.TWOSIDE) {
993	989	uint N = n1 + n2;
994	990	uint expected2 = n1 * n2;
…	…
1230	1226	}
1231	1227
1232
1233		real wilcoxonSignedRankPval(T)(T W, ulong N, Alt alt = Alt.TWOSIDE,
	1228	private real wilcoxonSignedRankPval(T)(T W, ulong N, Alt alt = Alt.TWOSIDE,
1234	1229	real tieSum = 0, uint exactThresh = 50)
1235	1230	in {
…	…
1237	1232	assert(tieSum >= 0 \|\| isNaN(tieSum));
1238	1233	} body {
	1234	if(alt == Alt.NONE) {
	1235	return real.nan;
	1236	}
	1237
1239	1238	if(tieSum == 0 && !isNaN(tieSum) && N <= exactThresh) {
1240	1239	return wilcoxSRPExact(cast(uint) W, cast(uint) N, alt);
…	…
1263	1262	* it would be more trouble than it's worth to write one generalized
1264	1263	* function.*/
1265		real wilcoxSRPExact(uint W, uint N, Alt alt = Alt.TWOSIDE) {
	1264	private real wilcoxSRPExact(uint W, uint N, Alt alt = Alt.TWOSIDE) {
1266	1265	uint expected2 = N * (N + 1) / 2;
1267	1266	switch(alt) {
…	…
1570	1569	real multiplier = 1;
1571	1570
	1571	// Normalize proportions to add up to the sum of the data.
1572	1572	if(countProp == Expected.PROPORTION) {
1573	1573	real expectSum = 0;
…	…
1712	1712	*
1713	1713	* Yates's continuity correction is never used in this implementation. If
1714		* you want something conservative, use fisherExact().
	1714	* you want something that's guaranteed to be conservative, use fisherExact().
1715	1715	*
1716	1716	* This is, for all practical purposes, an inherently non-directional test.
…	…
2182	2182	}
2183	2183
2184		real ksTestD(T, U)(T F, U Fprime)
	2184	private real ksTestD(T, U)(T F, U Fprime)
2185	2185	if(isInputRange!(T) && isInputRange!(U)) {
2186	2186	auto TAState = TempAlloc.getState;
…	…
2192	2192	}
2193	2193
2194		real ksTestDDestructive(T, U)(T F, U Fprime)
	2194	private real ksTestDDestructive(T, U)(T F, U Fprime)
2195	2195	if(isArrayLike!(T) && isArrayLike!(U)) {
2196	2196	qsort(F);
…	…
2217	2217	}
2218	2218
2219		real ksTestD(T, Func)(T Femp, Func F)
	2219	private real ksTestD(T, Func)(T Femp, Func F)
2220	2220	if(realInput!(T) && is(ReturnType!Func : real)) {
2221	2221	scope(exit) TempAlloc.free;
…	…
2223	2223	}
2224	2224
2225		real ksTestDDestructive(T, Func)(T Femp, Func F)
	2225	private real ksTestDDestructive(T, Func)(T Femp, Func F)
2226	2226	if(isArrayLike!(T) && is(ReturnType!Func : real)) {
2227	2227	qsort(Femp);
…	…
2237	2237	}
2238	2238
2239		real ksPval(ulong N, ulong Nprime, real D)
	2239	private real ksPval(ulong N, ulong Nprime, real D)
2240	2240	in {
2241	2241	assert(D >= -1);
…	…
2245	2245	}
2246	2246
2247		real ksPval(ulong N, real D)
	2247	private real ksPval(ulong N, real D)
2248	2248	in {
2249	2249	assert(D >= -1);
…	…
2275	2275	real runsTest(alias positive = "a > 0", T)(T obs, Alt alt = Alt.TWOSIDE)
2276	2276	if(isIterable!(T)) {
2277		~~Online~~RunsTest!(positive, IterType!(T)) r;
	2277	RunsTest!(positive, IterType!(T)) r;
2278	2278	foreach(elem; obs) {
2279	2279	r.put(elem);
2280	2280	}
2281		return r.p~~Val~~(alt);
	2281	return r.p(alt);
2282	2282	}
2283	2283
…	…
2295	2295	/**Runs test as in runsTest(), except calculates online instead of from stored
2296	2296	* array elements.*/
2297		struct ~~Online~~RunsTest(alias positive = "a > 0", T) {
	2297	struct RunsTest(alias positive = "a > 0", T) {
2298	2298	private:
2299	2299	uint nPos;
…	…
2336	2336
2337	2337	///
2338		real p~~Val~~(Alt alt = Alt.TWOSIDE) {
	2338	real p(Alt alt = Alt.TWOSIDE) {
2339	2339	uint N = nPos + nNeg;
2340	2340	real expected = 2.0L * nPos * nNeg / N + 1;
…	…
2361	2361	ConfInt pcorTest(T, U)(T range1, U range2, Alt alt = Alt.TWOSIDE, real confLevel = 0.95)
2362	2362	if(realInput!(T) && realInput!(U)) {
2363		~~Online~~Pcor res;
	2363	Pcor res;
2364	2364	while(!range1.empty && !range2.empty) {
2365	2365	res.put(range1.front, range2.front);
…	…
2440	2440	real sqN = sqrt(N - 3);
2441	2441	real z = sqN * atanh(cor);
2442		switch(alt) {
	2442
	2443	final switch(alt) {
2443	2444	case Alt.NONE :
2444	2445	return ret;
…	…
2461	2462	ret.upperBound = 1;
2462	2463	break;
2463		~~default:~~
2464		~~assert(0);~~
2465	2464	}
2466	2465	return ret;
…	…
2501	2500	}
2502	2501
2503		switch(alt) {
	2502	final switch(alt) {
2504	2503	case Alt.NONE :
2505	2504	return TestRes(tau);
…	…
2511	2510	case Alt.GREATER:
2512	2511	return TestRes(tau, normalCDFR(s - cc, 0, sd));
2513		~~default:~~
2514		~~assert(0);~~
2515	2512	}
2516	2513	}
…	…
2518	2515	// Dynamic programming algorithm for computing exact Kendall tau P-values.
2519	2516	// Thanks to ShreevatsaR from StackOverflow.
2520		real kcorExactP(uint N, uint swaps, Alt alt) {
	2517	private real kcorExactP(uint N, uint swaps, Alt alt) {
2521	2518	uint maxSwaps = N * (N - 1) / 2;
2522	2519	assert(swaps <= maxSwaps);
…	…
2674	2671	{
2675	2672	auto summ = summary(range);
2676		sqrtb1 = summ.skew;
	2673	sqrtb1 = summ.skewness;
2677	2674	b2 = summ.kurtosis + 3;
2678	2675	n = summ.N;

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