function?[ZE]?=?lrra（XAlambda）
%?This?routine?solves?the?following?nuclear-norm?optimization?problem
%?which?is?more?general?than?“lrr.m“
%?min?|Z|_*+lambda*|E|_21
%?s.t.?X?=?AZ+E
%?inputs:
%????????X?--?D*N?data?matrix?D?is?the?data?dimension?and?N?is?the?number
%?????????????of?data?vectors.
%????????A?--?D*M?matrix?of?a?dictionary?M?is?the?size?of?the?dictionary

if?nargin<3
????lambda?=?1;
end
tol?=?1e-8;
maxIter?=?1e6;
[d?n]?=?size（X）;
m?=?size（A2）;
rho?=?1.1;
max_mu?=?1e30;
mu?=?1e-6;
atx?=?A‘*X;
inv_a?=?inv（A‘*A+eye（m））;
%%?Initializing?optimization?variables
%?intialize
J?=?zeros（mn）;
Z?=?zeros（mn）;
E?=?sparse（dn）;

Y1?=?zeros（dn）;
Y2?=?zeros（mn）;
%%?Start?main?loop
iter?=?0;
disp（[‘initialrank=‘?num2str（rank（Z））]）;
while?iter????iter?=?iter?+?1;
????%update?J
????temp?=?Z?+?Y2/mu;
????[UsigmaV]?=?svd（temp‘econ‘）;
????sigma?=?diag（sigma）;
????svp?=?length（find（sigma>1/mu））;
????if?svp>=1
????????sigma?=?sigma（1:svp）-1