%?
%?Usage:??[A?[path]]=mexLasso（XDparam）;
%??or:????[A?[path]]=mexLasso（XQqparam）;
%
%?Name:?mexLasso
%
%?Description:?mexLasso?is?an?efficient?implementation?of?the
%?????homotopy-LARS?algorithm?for?solving?the?Lasso.?
%?????
%?????if?the?function?is?called?this?way?[A?[path]]=mexLasso（XDparam）
%?????it?aims?at?addressing?the?following?problems
%?????for?all?columns?x?of?X?it?computes?one?column?alpha?of?A
%?????that?solves
%???????1）?when?param.mode=0
%?????????min_{alpha}?||x-Dalpha||_2^2?s.t.?||alpha||_1?<=?lambda
%???????2）?when?param.mode=1
%?????????min_{alpha}?||alpha||_1?s.t.?||x-Dalpha||_2^2?<=?lambda
%???????3）?when?param.mode=2
%?????????min_{alpha}?0.5||x-Dalpha||_2^2?+?lambda||alpha||_1?+0.5?lambda2||alpha||_2^2
%
%?????if?the?function?is?called?this?way?[A?[path]]=mexLasso（XQqparam）
%?????it?solves?the?above?optimisation?problem?when?Q=D‘D?and?q=D‘x.
%
%?????Possibly?when?param.pos=true?it?solves?the?previous?problems
%?????with?positivity?constraints?on?the?vectors?alpha
%
%?Inputs:?X:??double?m?x?n?matrix???（input?signals）
%???????????????m?is?the?signal?size
%???????????????n?is?the?number?of?signals?to?decompose
%?????????D:??double?m?x?p?matrix???（dictionary）
%???????????????p?is?the?number?of?elements?in?the?dictionary
%?????????param:?struct
%???????????????param.lambda??（parameter）
%???????????????param.lambda2??（optional?parameter?for?solving?the?Elastic-Net）
%??????????????????????????????for?mode=0?and?mode=1?it?adds?a?ridge?on?the?Gram?Matrix
%???????????????param.L?（optional）?maximum?number?of?steps?of?the?homotopy?algorithm?（can
%????????????????????????be?used?as?a?stopping?criterion）
%???????????????param.pos?（optional?adds?non-negativity?constraints?on?the
%?????????????????coefficients?false?by?default）
%???????????????param.mode?（see?above?by?default:?2）
%???????????????param.numThreads?（optional?number?of?threads?for?exploiting
%?????????????????multi-core?/?multi-cpus.?By?default?it?takes?the?value?-1
%?????????????????which?automatically?selects?all?the?available?CPUs/cores）.
%???????????????param.cholesky?（optional?default?false）??choose?between?Cholesky?
%?????????????????implementation?or?one?based?on?the?matrix?inversion?Lemma
%???????????????param.ols?（optional?default?false）?perform?an?orthogonal?projection
%?????????????????before?returning?the?solution.
%???????????????param.max_length_path?（optional）?maximum?length?of?the?path?by?default?4*p
%
%?Output:?A:?double?sparse?p?x?n?matrix?（output?coefficients）
%?????????path:?optional??returns?the?regularisation?path?for?the?first?signal
%
%?Note:?this?function?admits?a?few?experimental?usages?which?have?not
%?????been?extensively?tested:
%?????????-?single?precision?setting?（even?though?the?output?alpha?is?double?
%???????????precision）
%
%?Author:?Julien?Mairal?2009

?屬性????????????大小?????日期????時間???名稱
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?????文件???????2843??2012-05-18?01:16??mexLasso.m

?????文件?????182272??2013-11-24?16:15??mexLasso.mexw64

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???????????????185115????????????????????2