function?[XrhoetaF]?=?cgls（Abkreorths）?
%CGLS?Conjugate?gradient?algorithm?applied?implicitly?to?the?normal?equations.?
%?
%?[XrhoetaF]?=?cgls（Abkreorths）?
%?
%?Performs?k?steps?of?the?conjugate?gradient?algorithm?applied?
%?implicitly?to?the?normal?equations?A‘*A*x?=?A‘*b.?
%?
%?The?routine?returns?all?k?solutions?stored?as?columns?of?
%?the?matrix?X.??The?corresponding?solution?and?residual?norms?
%?are?returned?in?the?vectors?eta?and?rho?respectively.?
%?
%?If?the?singular?values?s?are?also?provided?cgls?computes?the?
%?filter?factors?associated?with?each?step?and?stores?them?
%?columnwise?in?the?matrix?F.?
%?
%?Reorthogonalization?of?the?normal?equation?residual?vectors?
%?A‘*（A*X（:i）-b）?is?controlled?by?means?of?reorth:?
%????reorth?=?0?:?no?reorthogonalization?（default）?
%????reorth?=?1?:?reorthogonalization?by?means?of?MGS.?
?
%?References:?A.?Bjorck?“Numerical?Methods?for?Least?Squares?Problems“?
%?SIAM?Philadelphia?1996.?
%?C.?R.?Vogel?“Solving?ill-conditioned?linear?systems?using?the?
%?conjugate?gradient?method“?Report?Dept.?of?Mathematical?
%?Sciences?Montana?State?University?1987.?
??
%?Per?Christian?Hansen?IMM?April?8?2001.?
?
%?The?fudge?threshold?is?used?to?prevent?filter?factors?from?exploding.?
fudge_thr?=?1e-4;?
??
%?Initialization.?
if?（k?if?（nargin==3）?reorth?=?0;?end?
if?（nargout==4?&?nargin<5）?error（‘Too?few?input?arguments‘）?end?
if?（reorth<0?|?reorth>1）?error（‘Illegal?reorth‘）?end?
[mn]?=?size（A）;?X?=?zeros（nk）;?
if?（reorth==1）?ATr?=?zeros（nk）;?end?
if?（nargout?>?1）?
??eta?=?zeros（k1）;?rho?=?eta;?
end?
if?（nargin==5）?
??F?=?zeros（nk）;?Fd?=?zeros（n1）;?s2?=?s.^2;?
end?
?
%?Prepare?for?CG?iteration.?
x?=?zeros（n1）;?
d?=?（b‘*A）‘;???%?A‘*b;?
r?=?b;?
normr2?=?d‘*d;?
if?（reorth==1）?ATr（:1）?=?d/norm（d）;?end?
?
%?Iterate.?
for?j=1:k?
?
??%?Update?x?and?r?vectors.?
??Ad?=?A*d;?alpha?=?normr2/（Ad‘*Ad）;?
??x??=?x?+?alpha*d;?
??r??=?r?-?alpha*Ad;?
??s??=?（r‘*A）‘;???%?A‘*r;?
?
??%?Reorthogonalize?s?to?previous?s-vectors?if?required.?
??if?（reorth==1）?
????for?i=1:j-1?s?=?s?-?（ATr（:i）‘*s）*ATr（:i）;?end?
????ATr（:j）?=?s/norm（s）;?
??end?
?
??%?Update?d?vector.?
??normr2_new?=?s‘*s;?
??beta?=?normr2_new/normr2;?
??normr2?=?normr2_new;?
??d?=?s?+?beta*d;?
??X（:j）?=?x;?
???
??%?Compute?norms?if?required.?
??if?（nargout>1）?rho（j）?=?norm（r）;?end?
??if?（nargout>2）?eta（j）?=?norm（x）;?end?
?
??%?Compute?filter?factors?if?required.?
??if?（nargin==5）?
????if?（j==1）?
??????F（:1）?=?alpha*s2;?
??????Fd?=?s2?-?s2.*F（:1）?+?beta*s2;?
????else?
??????F（:j）?=?F（:j-1）?+?alpha*Fd;?
??????Fd?=?s2?-?s2.*F（:j）?+?beta*Fd;?
????end?
????if?（j?>?2）?
??????f?=?find（abs（F（:j-1）-1）???????if?（length（f）?>?0）?F（fj）?=?ones（length（f）1）;?end?
????end?
??end?
?
end?

?屬性????????????大小?????日期????時(shí)間???名稱
-----------?---------??----------?-----??----

?????文件???????2851??2002-08-26?16:03??ERT\cgls.m

?????文件?????859901??2013-08-30?20:35??ERT\cirs.mat

?????文件???????7445??2013-12-25?20:38??ERT\Currenteit.m

?????文件??????21628??2013-08-30?20:07??ERT\empty-model.mphbin

?????文件?????997626??2012-09-02?19:01??ERT\ert仿真操作過程_comsol.pdf

?????文件????????361??2014-03-01?16:01??ERT\inversecgls.m

?????文件???????1719??2013-12-25?21:22??ERT\JacobianERT.m

?????文件???????5311??2013-12-25?20:53??ERT\measure.m

?????文件???????3528??2013-08-30?20:56??ERT\measure1.m

?????文件????????610??2013-12-25?21:35??ERT\nodeeit.m

?????文件???????1432??2013-08-30?20:35??ERT\num.mat

?????文件???????5534??2013-09-01?16:08??ERT\text.m

?????文件???????3939??2013-08-30?19:00??ERT\text1.m

?????文件???????1719??2013-08-30?20:35??ERT\uel.mat

?????文件???????1682??2013-08-30?20:35??ERT\uref.mat

?????文件????????492??2013-08-30?20:36??ERT\xy.mat

?????文件????????130??2013-08-30?18:55??ERT\新建文本文檔.txt

?????目錄??????????0??2014-11-12?18:20??ERT

-----------?---------??----------?-----??----

??????????????1915908????????????????????18