function?[pY]?=?approximation_order（Hn）

%?APPROXIMATION_ORDER?--?compute?approximation?order?and?approximation?vectors
%
%????????[pY]?=?approximation_order（H）
%
%?This?routine?determines?the?approximation?order?of?a?refinable?
%?function?vector?as?well?as?the?approximation?vectors.
%?The?vectors?are?returned?in?the?columns?of?a?matrix?Y.
%
%?H?can?be?a?symbol?（of?the?multiscaling?function?alone?or?of?the
%?entire?multiwavelet）?or?a?polyphase?matrix.

%?Algorithm:
%
%?This?routine?is?based?on?the?sum?rules?in?terms?of?partial?moments.
%?Instead?of?solving?for?y_0?y_1?...?in?turn?we?solve?for?all
%?y_k?k=0...p-1?simultaneously?until?it?doesn‘t?work?any?more
%?for?some?p.
%
%?So?when?we?calculate?y_2?we?recompute?y_0?and?y_1.?What‘s?the?point?
%?In?numerical?experiments?years?ago?I?ran?into?cases?where?you?can
%?get?multiple?solutions?for?y_1?for?example?but?when?you?look
%?for?y_2?only?one?of?the?y_1?works.
%
%?I?never?completely?figured?out?why?this?happens.?Most?likely?these
%?scaling?functions?are?not?stable.?Anyway?this?routine?will?continue
%?when?multiple?solutions?are?found?and?hope?they?will?go?away?at
%?a?later?point.?It?does?print?warning?messages?when?this?happens.

%?Copyright?（c）?2004?by?Fritz?Keinert?（keinert@iastate.edu）
%?Dept.?of?Mathematics?Iowa?State?University?Ames?IA?50011.
%?This?software?may?be?freely?used?and?distributed?for?non-commercial
%?purposes?provided?this?copyright?statement?is?preserved?and
%?appropriate?credit?for?its?use?is?given.
%
%?Last?update:?Feb?20?2004

%?convert?H?into?the?symbol?of?the?refinable?function?vector?alone
H?=?symbol（H）;
r?=?H.r;
m?=?H.m;
H?=?H（1:r:）;
H?=?trim（H）;

%?check?for?approximation?order?1
M?=?mpoly（partial_moment（H0）‘）;
I?=?kron（ones（m1）eye（r））;

A?=?M{0}?-?I/m;
y?=?nullspace（A）;

if?（size（y2）?>?1）
????disp（‘multiple?y_0?found‘）;
end

if?（size（y2）?==?0）
????p?=?0;
????Y?=?zeros（r0）;
????return
end


%?check?for?higher?orders

for?p?=?1:1000?
????M{p}?=?partial_moment（Hp）‘;
????for?s?=?0:p
	A（p*r*m+1:（p+1）*r*ms*r+1:（s+1）*r）?=?binomial（ps）*（-1）^（p-s）*m^s*M{p-s};
????end
????A（p*r*m+1:（p+1）*r*mp*r+1:（p+1）*r）?=?A（p*r*m+1:（p+1）*r*mp*r+1:（p+1）*r）?-?I/m;
????ynew?=?nullspace（A）;

????if?（size（ynew2）?>?1）
	disp（[‘multiple?y_‘num2str（p）‘?found‘]）;
????end

????if?（size（ynew2）?==?0）
	break
????end
????
????y?=?ynew;
end

%?try?to?find?more?vectors?if?requested

if?（nargin?????n?=?p;
end

if?（n?>?p）
????M?=?mpoly（moment（H0）‘）;
????for?j?=?1:p-1
	Mp?=?moment（Hj）;
	M{j}?=?Mp‘;
????end
????A?=?A（1:p*r*m1:p*r）;
end

for?j?=?p:n-1
????Mp?=?moment（Hj）;
????M{j}?=?Mp‘;
????for?s?=?0:j
	B（（j-p）*r+1:（j-p+1）*rs*r+1:（s+1）*r）?=?binomial（js）?*?（-1）^（j-s）*m^s*M{j-s};
????end
????B（（j-p）*r+1:（j-p+1）*rj*r+1:（j+1）*r）?=?B（（j-p）*r+1:（j-p+1）*rj*r+1:（j+1）*r）?-?eye（r）;
????ynew?=?nullspace（[Azeros（p*m*r（j-p+1）*r）;B]）;
????if?（size（ynew2）?>?1）
	disp（[

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

?????文件???????1025??2004-02-21?16:43??Wavelets?and?Multiwavelets\@double\binomial.m

?????文件????????595??2004-02-21?16:44??Wavelets?and?Multiwavelets\@double\factorial.m

?????文件????????650??2004-02-21?16:44??Wavelets?and?Multiwavelets\@double\isidentity.m

?????文件????????614??2004-02-21?16:44??Wavelets?and?Multiwavelets\@double\issingular.m

?????文件????????897??2004-02-21?16:44??Wavelets?and?Multiwavelets\@double\issymbolic.m

?????文件????????859??2004-02-21?16:44??Wavelets?and?Multiwavelets\@double\iszero.m

?????目錄??????????0??2005-07-04?10:56??Wavelets?and?Multiwavelets\@double

?????文件????????936??2004-02-21?16:47??Wavelets?and?Multiwavelets\@mpoly\ceil.m

?????文件????????973??2004-02-21?16:47??Wavelets?and?Multiwavelets\@mpoly\ctranspose.m

?????文件????????843??2004-02-21?16:47??Wavelets?and?Multiwavelets\@mpoly\det.m

?????文件????????724??2004-02-21?16:47??Wavelets?and?Multiwavelets\@mpoly\diag.m

?????文件???????1266??2004-02-21?16:47??Wavelets?and?Multiwavelets\@mpoly\display.m

?????文件????????721??2004-02-21?16:47??Wavelets?and?Multiwavelets\@mpoly\double.m

?????文件????????915??2004-02-21?16:47??Wavelets?and?Multiwavelets\@mpoly\end.m

?????文件????????600??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\eq.m

?????文件????????854??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\expand.m

?????文件????????921??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\fix.m

?????文件????????943??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\floor.m

?????文件???????1599??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\get.m

?????文件???????1924??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\horzcat.m

?????文件????????727??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\inv.m

?????文件????????541??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\isconstant.m

?????文件????????666??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\isidentity.m

?????文件????????519??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\ismonomial.m

?????文件????????595??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\isnumeric.m

?????文件????????709??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\issymbolic.m

?????文件????????872??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\iszero.m

?????文件???????2025??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\kron.m

?????文件???????1898??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\ldivide.m

?????文件???????1090??2004-02-21?16:48??Wavelets?and?Multiwavelets\@mpoly\longinv.m

............此處省略84個文件信息