changes

求解离散病态问题的正则化方法matlab 工具箱

***************************************************************
* This is Version 3.0 of Regularization Tools for Matlab 5.2  *
*-------------------------------------------------------------*
*                 Per Christian Hansen, IMM                   *
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Revisions in Version 1.1

07/14/92
Fixed a bug in l_curve (beta2 was not computed correct).
Fixed the same bug in gcv and lagrange.
Fixed a bug in mtsvd (beta was never computed).

09/11/92
Fixed a typo in l_curve.
Added more pause statements in regudemo as a courtesy to PC users.

Revisions in Version 1.2

09/17/92
Fixed non-standard use of zeros and ones.
Added more comments to the test problems.

Revisions in Version 1.3

11/05/92
Changed routines cg and pcg, based on an algorithm from Louis's book,
to routines cgls and pcgls based on an algorithm from Bjorck's book.

02/09/93
New subroutine names: changed cg, pcg, and tls to cgls, pcgls, and ttls.

02/26/93
Minor bug in fil_fac corrected.

03/12/93:
Fixed minor bug in plot_lc.

03/16/93:
Added H1 lines to all routines.
Renamed squire to foxgood.
Routine ttls now computes the correct TLS residual.
Hold state is now restored after all plots.
Error messages in l_corner and l_curve if Spline Toolbox is not available.

04/21/93:
Modified gen_form and std_form.

05/26/93:
Modified input chech in lanc_b, lsqr, and plsqr.
Changed to sparse storage of L.

06/12/93:
Fixed bug in gen_form for square L_p.

06/23/93:
Added ttls filter factors to fil_fac.

10/29/93:
Added 10 dummy subroutines for the case when Spline Toolbox is not installed.

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|      Changes after Regu Tools has appeared in NumerAlgo.      |
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02/01/94:
Fixed bug in cgls (s -> s2).

08/03/94:
Expanded stopping criterion in newton.

08/09/94:
Revised comment lines in maxent.

10/07/94:
Removed superfluorus statements in mtsvd.

11/01/94:
Modified get_l slightly such that the sign of L*x is correct.

02/09/95:
Revised qr in csd, l_curve and mtsvd to compute "economy size" decomposition.
Renamed csd to csdecomp (csd is now a function in the Signal Proc. Toolbox).
Revised gsvd to call csdecomp.

11/08/95:
Fixed bug in csdecomp when p=1.

03/22/96:
Changed tsvd and tgsvd to allow k=0.

10/08/96:
Changed tgsvd to allow a square L.

10/22/96:
Changed tikhonov to allow a square L.

04/17/97:
Replaced (..==NaN) with isnan(..) in bsvd.
Added initialization of U2t in csdecomp.

04/21/97:
Changed variable name "case" to "example" in deriv2.
Changed meshdom to meshgrid in spikes, and deleted the flipud command.
Changed variable xi to eta in picard.

06/30/97:
Removed function bsvd (obsolete with sparse format of bidiagonal matrices).
Changed to sparse format of bidiagonal matrix in bidiag.
Changed to sparse format of bidiagonal matrix in lanc_b.
Added function regutm.

07/02/97:
Added reorthogonalization of normal eq. residual vectors to cgls and pcgls.
Fixed bug in pcgls when computing filter factors.

07/29/97:
Changed variable name in pinit.
Modified lsolve, ltsolve, and std_form according to simpler formulas.

09/18/97:
Added blur test problem.
Deleted mgs, and included the MGS process in get_l.

11/11/97:
Modified gen_hh to compensate for Matlab's signum function.

12/22/97:
Replaced gsvd with cgsvd, and deleted csdecomp.
Added more output arguments to dsvd, mtsvd, tgsvd, tikhonov, and tsvd.
Added method = 'ttls' to fil_fac.
Improved the plots in gcv, lagrange, picard, plot_lc, and quasiopt.
Added input parameter x_0 to tikhonov.

12/29/97:
Added call to fmin in gcv, l_curve, and quasiopt.
Corrected bugs in discrep and lsqi.
Modified heb_new and newton to work with lambda instead of lambda squared.

02/05/98:
Added d==0 to get_l.

04/16/98:
Modified l_corner and spleval to be consistent with Spline Toolbox v. 2.0.