function?[knotsk]?=?aptknt（tauk）
%APTKNT?Acceptable?knot?sequence
%
%???APTKNT（TAUK）??returns?for?a?given?nondecreasing?sequence?TAU?with
%???TAU（i）?%???Schoenberg-Whitney?conditions
%
%????????????KNOTS（i）?%
%???hold?（with?equality?only?for?the?first?or?last?knot）?ensuring?that
%???the?space?of?splines?of?order?
%??????????????K??:=??min（Klength（TAU））??
%???with?knot?sequence?KNOTS?has?a?unique?interpolant?to?arbitrary?data
%???at?the?data?sites?TAU;?the?K?used?is?optionally?returned.
%
%???For?example?for?strictly?increasing??x??and?given?corresponding??y?
%
%??????sp?=?spapi（aptknt（xk）xy）;
%
%???gives?a?spline?f??of?order??min（klength（x））??satisfying?f（x（i））?=?y（i）
%???all?i?（and?the?same?result?is?obtained?by?spapi（kxy）?）.
%???Be?aware?though?of?the?fact?that?for?highly?nonuniform??x??the?
%???determination?of?this?spline?can?be?ill-conditioned?leading?possibly
%???to?very?strange?behavior?away?from?the?interpolation?points.
%
%???At?present?the?knot?sequence?chosen?here?is?the?initial?guess?used?for
%???the?iterative?determination?of?the?‘optimal‘?knots?in?OPTKNT.
%
%???See?also?AUGKNT?AVEKNT?NEWKNT?OPTKNT.

%???Copyright?1987-2008?The?MathWorks?Inc.
%???$Revision:?1.1.6.1?$??$Date:?2009/12/22?18:48:34?$

%?If??tau（1）?<=?...?<=?tau（n）?with?no?more?than??k-2??consecutive?equalities
%?and??n>k??then?the?output??xi?=?aveknt（tauk）??is?strictly?increasing?and
%?for?any?a%?the?above?Schoenberg-Whitney?conditions?wrto??tau?.?
%
%?Indeed?then??
%??????????????????knots（1:k）?=?a?%?while?for??i=1:n-k
%???????????knots（k+i）?=??xi（i）?=?（tau（i+1）+...+tau（i+k-1））/（k-1）?
%?hence?（using?the?fact?that?at?most?k-1?consecutive?tau‘s?can?be?equal）
%?????????????????tau（i）?%?and?finally
%???????????????tau（n-k+1）?<=?...?<=?tau（n）?%?Letting?now??a?-->??tau（1）??and??b?-->?tau（end）??will?not?change?any?of?these
%?inequalities?except?those?involving?the?first?and?last?data?site?may?not
%?be?strict?any?more.?But?that?is?ok?since?these?will?be?the?endpoints?of?the
%?corresponding?basic?interval?hence?only?right?respectively?left?limits
%?matter?there.

n?=?length（tau）;?
if?n<2?error（‘SPLINES:APTKNT:toofewTAU‘?...
??????????????‘There?must?be?at?least?two?（distinct）?sites.‘）?end

k?=?max（1min（kn））;?dtau?=?diff（tau）;
if?any（dtau<0）
???error（‘SPLINES:APTKNT:TAUdecreasing‘?...
?????????‘The?site?sequence?must?be?nondecreasing.‘）?end
if?k==1?%?simply?use?midpoints?between?data?sites
???if?~all（dtau）
??????error（‘SPLINES:APTKNT:TAUmulttoolarge‘?...
????????????‘For?k==1?the?site?sequence?must?be?strictly?increasing.‘）
???end
???knots?=?[tau（1）?tau（1:n-1）+dtau/2?tau（n）];
else
???if?any（tau（k:n）==tau（1:n-k+1））
??????error（‘SPLINES:APTKNT:TAUmulttoolarge‘?...
??????????

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????3124??2009-12-22?13:48??splines\aptknt.m

?????文件???????2084??2009-12-22?13:48??splines\augknt.m

?????文件???????1057??2009-12-22?13:48??splines\aveknt.m

?????文件???????2166??2009-12-22?13:48??splines\bkbrk.m

?????文件???????1464??2009-12-22?13:48??splines\brk2knt.m

?????文件???????1692??2009-12-22?13:48??splines\bspline.m

?????文件???????4903??2009-12-22?13:48??splines\chbpnt.m

?????文件???????9289??2009-12-22?13:48??splines\chckxywp.m

?????文件???????4520??2010-08-03?17:45??splines\Contents.m

?????文件??????10322??2009-12-22?13:48??splines\csape.m

?????文件???????4708??2009-12-22?13:48??splines\csapi.m

?????文件??????11713??2009-12-22?13:48??splines\csaps.m

?????文件???????2611??2009-12-22?13:48??splines\cscvn.m

?????文件???????8805??2009-12-22?13:48??splines\fn2fm.m

?????文件???????6536??2009-12-22?13:48??splines\fnbrk.m

?????文件???????1436??2009-12-22?13:48??splines\fnchg.m

?????文件??????20459??2010-04-24?14:06??splines\fncmb.m

?????文件???????5350??2009-12-22?13:48??splines\fnder.m

?????文件???????3952??2009-12-22?13:48??splines\fndir.m

?????文件???????3514??2009-12-22?13:48??splines\fnint.m

?????文件???????3065??2009-12-22?13:48??splines\fnjmp.m

?????文件???????2117??2009-12-22?13:49??splines\fnmin.m

?????文件???????7537??2009-12-22?13:49??splines\fnplt.m

?????文件???????2489??2009-12-22?13:49??splines\fnrfn.m

?????文件???????8121??2009-12-22?13:49??splines\fntlr.m

?????文件???????3714??2009-12-22?13:49??splines\fnval.m

?????文件???????5352??2009-12-22?13:49??splines\fnxtr.m

?????文件??????14423??2010-06-11?11:49??splines\fnzeros.m

?????文件????????661??2009-12-22?13:49??splines\franke.m

?????文件???????1425??2009-12-22?13:49??splines\getcurve.m

............此處省略126個文件信息