function?[USVnumiter]??=?FPC（nOmegabmu_finalmaxitertol）
%?[USigmaVnumiter]??=?FPC（nOmegabmu_finalmaxitergtol）
%
%?Finds?mininum??mu?||X||_*?+?1/2?||?A（X）?-?b?||_2^2
%
%???where?A（X）?is?the?projection?of?X?onto?the?set?of?indices
%???in?Omega.
%
%?For?efficiency?the?algorithm?uses?continuation?（i.e.?a?series?of
%???mu?aka?the?“outer?loop“）?until?mu?=?mu_final.
%
%?maxiter?controls?maximum?number?of?iterations?per?inner?loop
%
%?Outputs:
%???UV?and?Sigma?are?singular?vectors?and?singular?values?where
%???????X?=?U*Sigma*V‘
%???numiter?is?the?number?of?iterations?over?all?inner?and?outer?loops

%?Reference:
%
%???“Fixed?point?and?Bregman?iterative?methods?for?matrix
%???????rank?minimization.“
%???Shiquian?Ma?Donald?Goldfarb?Lifeng?Chen?October?2008
%???ftp://ftp.math.ucla.edu/pub/camreport/cam08-78.pdf

%?code?by?Stephen?Becker?srbecker@caltech.edu?March?2009

%?May?2009:?adding?support?for?complex?matrices


%?--?some?parameters:
tau?=?1.99;??%?recommended?that?tau?is?between?1?and?2
eta_mu?=?1/4;???%?how?much?to?decrease?mu?at?every?step

%VERBOSE?=?false;??%?no?output
VERBOSE?=?1;????%?a?little?bit?of?output
VERBOSE?=?2;????%?even?more?output



if?nargin?????tol?=?1e-4;
end
if?nargin?????maxiter?=?500;
end
????
if?length（n）?==?1
????n1?=?n（1）;?n2?=?n1;
elseif?length（n）?==?2
????n1?=?n（1）;?n2?=?n（2）;
end
if?n1*n2?????SMALLSCALE?=?true;?
????X?=?zeros（n1n2）;
else
????SMALLSCALE?=?false;
end


m?=?length（Omega）;?[tempindx]?=?sort（Omega）;?
incre?=?5;
r?=?1;?s?=?r?+?1;??%?estimate?new?rank
normb?=?norm（b）;

[i?j]?=?ind2sub（[n1n2]?Omega）;
G?=?sparse（ijbn1n2m）;??%?i.e.?starting?with?X?=?0;
mu?=?normest（?G??1e-2?）;

%?What?the?best?way?to?multiply?a?sparse?matrix?
[forwardType?transposeType]?=?findBestMultiply（G.2）;

U?=?zeros（n11）;
V?=?zeros（n21）;
S?=?0;
relResid?=?2;

if?VERBOSE?fprintf（‘**************************************\n‘）;?end
numiter?=?0;
while?mu?>?mu_final
????mu?=?max（mu?*?eta_mumu_final）;
????if?VERBOSE?fprintf（‘FPC?mu?=?%f\n‘mu）;?end
????if?VERBOSE?==?1?fprintf（‘\tIteration:??????‘）;?end
????s?=?2*r?+?1;??%?estimate?new?rank?for?next?iteration
for?k?=?1:maxiter
????numiter?=?numiter?+?1;
????if?VERBOSE==1?fprintf（‘\b\b\b\b%4d‘k）;??end

????%?Make?routines?for?multiplying?by?a?sparse?matrix
????Gt?=?G‘;
????switch?forwardType
????????case?1?Gforward?=?@（x）?G*x;
????????case?2?Gforward?=?@（x）?Gt‘*x;
????????case?3?Gforward?=?@（x）?smvp（Gx）;
????end
????switch?transposeType?
????????case?1?Gtranspose?=?@（x）?Gt*x;
????????case?2?Gtranspose?=?@（x）?G‘*x;
????????case?3?Gtranspose?=?@（x）?smvp（Gtx）;
????end
????
????%?Y?=?X?-?tau*G
????Y?=?@（x）?U*（S*（V‘*x））?-?tau*Gforward（x）;
????Yt=?@（x）?V*（S*（U‘*x））?-?tau*Gtranspose（x）;
????
????%?Perform?a?SVD
????if?SMALLSCALE
????????[USigmaV]?=?svd（full（X?-?tau*G）‘econ‘）;
????else
????????OK?=?0;
????????while?~OK
????????????opts?=?[];?
????????????if?~isreal（G）?opts.eta?=?1e-16;?end
%?????

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????7036??2009-05-27?22:59??SVT.m
?????文件????????5167??2009-05-27?23:03??FPC.m
?????文件????????3904??2009-05-27?23:00??Test_SVT.m
?????文件?????????985??2009-02-22?02:15??private\bdsqr.m
?????文件???????11748??2009-05-20?17:17??private\bdsqr.mexa64
?????文件????????3016??2009-03-24?16:20??private\bdsqr_mex.c
?????文件????????8049??2009-05-28?01:12??private\bdsqr.mexglx
?????文件???????14072??2009-03-04?20:44??private\bdsqr.mexmaci
?????文件???????25208??2009-02-22?02:15??private\bdsqr.mexsg
?????文件???????26109??2009-02-22?02:15??private\bdsqr.mexsg64
?????文件???????95852??2009-02-22?02:15??private\bdsqr.mexsol
?????文件???????55808??2009-03-14?23:23??private\bdsqr.mexw32
?????文件????????1504??2009-03-14?23:23??private\compute_int.m
?????文件????????1346??2009-02-22?02:15??private\dbdqr.c
?????文件?????????445??2009-02-22?02:15??private\dbdqr.f
?????文件????????2056??2009-05-13?23:31??private\findBestMultiply.m
?????文件???????14907??2009-05-28?01:12??private\install_mex.m
?????文件???????23704??2009-05-14?00:02??private\lanbpro.m
?????文件???????11964??2009-05-13?23:32??private\lansvd.m
?????文件?????????939??2009-03-04?22:44??private\refinebounds.m
?????文件????????3488??2009-03-08?01:58??private\reorth.c
?????文件????????2906??2009-05-13?23:33??private\reorth_complex.m
?????文件????????3580??2009-03-04?22:44??private\reorth.f
?????文件????????2661??2009-03-04?22:44??private\reorth.m
?????文件???????12000??2009-05-20?17:17??private\reorth.mexa64
?????文件????????3573??2009-03-24?16:15??private\reorth_mex.c
?????文件????????8069??2009-05-28?01:12??private\reorth.mexglx
?????文件???????21268??2009-03-04?22:44??private\reorth.mexmaci
?????文件???????25428??2009-03-04?22:44??private\reorth.mexsg
?????文件???????26694??2009-03-04?22:44??private\reorth.mexsg64
?????文件???????86872??2009-03-04?22:44??private\reorth.mexsol
............此處省略22個文件信息