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Highlights from
regtools

app_hh(A,beta,v) APP_HH Apply a Householder transformation.
art(A,b,k) ART Algebraic reconstruction technique (Kaczmarz's method).
baart(n) BAART Test problem: Fredholm integral equation of the first kind.
bidiag(A) BIDIAG Bidiagonalization of an m-times-n matrix with m >= n.
blur(N,band,sigma) BLUR Test problem: digital image deblurring.
cgls(A,b,k,reorth,s) CGLS Conjugate gradient algorithm applied implicitly to the normal equations.
cgsvd(A,L) CGSVD Compact generalized SVD of a matrix pair in regularization problems.
corner(rho,eta,fig) CORNER Find corner of discrete L-curve via adaptive pruning algorithm.
csvd(A,tst) CSVD Compact singular value decomposition.
deriv2(n,example) DERIV2 Test problem: computation of the second derivative.
discrep(U,s,V,b,delta,x_0) DISCREP Discrepancy principle criterion for choosing the reg. parameter.
dsvd(U,s,V,b,lambda) DSVD Damped SVD and GSVD regularization.
fil_fac(s,reg_param,method,s1... FIL_FAC Filter factors for some regularization methods.
foxgood(n) FOXGOOD Test problem: severely ill-posed problem.
gcv(U,s,b,method) GCV Plot the GCV function and find its minimum.
gcvfun(lambda,s2,beta,delta0,...
gen_form(L_p,x_s,A,b,K,M) GEN_FORM Transform a standard-form problem back to the general-form setting.
gen_hh(x) GEN_HH Generate a Householder transformation.
get_l(n,d) GET_L Compute discrete derivative operators.
gravity(n,example,a,b,d) GRAVITY Test problem: 1-D gravity surveying model problem
heat(n,kappa) HEAT Test problem: inverse heat equation.
i_laplace(n,example) I_LAPLACE Test problem: inverse Laplace transformation.
l_corner(rho,eta,reg_param,U,... L_CORNER Locate the "corner" of the L-curve.
l_curve(U,sm,b,method,L,V) L_CURVE Plot the L-curve and find its "corner".
lagrange(U,s,b,more) LAGRANGE Plot the Lagrange function for Tikhonov regularization.
lanc_b(A,p,k,reorth) LANC_B Lanczos bidiagonalization.
lcfun(lambda,s,beta,xi,fifth) Auxiliary routine for l_corner; computes the NEGATIVE of the curvature.
lsolve(L,y,W,T) LSOLVE Utility routine for "preconditioned" iterative methods.
lsqi(U,s,V,b,alpha,x_0) LSQI Least squares minimizaiton with a quadratic inequality constraint.
lsqr_b(A,b,k,reorth,s) LSQR_B Solution of least squares problems by Lanczos bidiagonalization.
ltsolve(L,y,W,T) LTSOLVE Utility routine for "preconditioned" iterative methods.
maxent(A,b,lambda,w,x0) MAXENT Maximum entropy regularization.
mr2(A,b,k,reorth) MR2 Solution of symmetric indefinite problems by the MR-II algorithm
mtsvd(U,s,V,b,k,L) MTSVD Modified truncated SVD regularization.
ncp(U,s,b,method) NCP Plot the NCPs and find the one closest to a straight line.
ncpfun(lambda,s,beta,U,dsvd)
nu(A,b,k,nu,s) NU Brakhage's nu-method.
parallax(n) PARALLAX Stellar parallax problem with 28 fixed, real observations.
pcgls(A,L,W,b,k,reorth,sm) PCGLS "Precond." conjugate gradients appl. implicitly to normal equations.
phillips(n) PHILLIPS Test problem: Phillips' "famous" problem.
picard(U,s,b,d) PICARD Visual inspection of the Picard condition.
pinit(W,A,b) PINIT Utility init.-procedure for "preconditioned" iterative methods.
plot_lc(rho,eta,marker,ps,reg... PLOT_LC Plot the L-curve.
plsqr_b(A,L,W,b,k,reorth,sm) PLSQR_B "Precond." version of the LSQR Lanczos bidiagonalization algorithm.
pmr2(A,L,N,b,k,reorth) PMR2 Preconditioned MR-II algorithm for symmetric indefinite problems
pnu(A,L,W,b,k,nu,sm) PNU "Preconditioned" version of Brakhage's nu-method.
prrgmres(A,L,N,b,k) PRRGMRES Preconditioned RRGMRES algorithm for square inconsistent systems
quasifun(lambda,s,xi,dsvd)
quasiopt(U,s,b,method) QUASIOPT Quasi-optimality criterion for choosing the reg. parameter
regutm(m,n,s) REGUTM Test matrix for regularization methods.
rrgmres(A,b,k) RRGMRES Range-restricted GMRES algorithm for square inconsistent systems
shaw(n) SHAW Test problem: one-dimensional image restoration model.
spikes(n,t_max) SPIKES Test problem with a "spiky" solution.
spleval(f) SPLEVAL Evaluation of a spline or spline curve.
splsqr(A,L,b,lambda,Vsp,maxit... SPLSQR Subspace preconditioned LSQR for discrete ill-posed problems.
splsqr(A,b,lambda,Vsp,maxit,t... SPLSQR Subspace preconditioned LSQR for discrete ill-posed problems.
std_form(A,L,b,W) STD_FORM Transform a general-form reg. problem into one in standard form.
tgsvd(U,sm,X,b,k) TGSVD Truncated GSVD regularization.
tikhonov(U,s,V,b,lambda,x_0) TIKHONOV Tikhonov regularization.
tomo(N,f) TOMO Create a 2D tomography test problem
tsvd(U,s,V,b,k) TSVD Truncated SVD regularization.
ttls(V1,k,s1) TTLS Truncated TLS regularization.
ursell(n) URSELL Test problem: integral equation wiht no square integrable solution.
wing(n,t1,t2) WING Test problem with a discontinuous solution.
Contents.m
regudemo.m
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regtools

by Per Christian Hansen

16 Apr 1998 (Updated 18 Mar 2008)

Analysis and Solution of Discrete Ill-Posed Problems.

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Description

Regularization Tools: A MATLAB package for Analysis and Solution of Discrete Ill-Posed Problems. Version 4.1.

By means of the routines in this package, the user can experiment with different regularization strategies. The package also includes 12 test problems.

Requires Matlab Version 7.3. The manual and more details can be found at

http://www2.imm.dtu.dk/~pch/Regutools/

Acknowledgements

This submission has inspired the following:
NLCSmoothReg

MATLAB release

MATLAB 7.5 (R2007b)

Tags for This File
Everyone's Tags	discrete(4), illposed(2), linear algebra, mathematics, regularization(2)
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Comments and Ratings (18)
30 Sep 2001	Brian Borchers	This is a very useful package of tools for the regularization of linear inverse problems. I've found this package to be very useful both in research and in teaching a course in inverse problems. One minor complaint- the author has released an updated version for MATLAB 6 which isn't on MATLAB Central yet.
21 Oct 2001	Volker Rath	Indispensable for everybody working on inverse problems.
28 Nov 2001	Wlodek Tych	Excellent tool, good documentation. As with other powerful methods you have to know what you are doing. Many thanks to the Author for writing and sharing.
25 Jan 2002	Ben Fisher	Great collection of tools. It needs some time to get familiarised with all functions though the documentaion is good.
09 Apr 2003	Dr.Feras AL-Faqih
03 Nov 2003	Valeriy Kruchko	Thank you for this job.
07 Mar 2004	Nicolas MARIE	Thank you for this very useful package.
23 Jul 2004	Ruslan Pechenkin	Thanks a lot, it is very useful
06 Mar 2007	abdel jardani	merci
10 Apr 2007	sdfasf kjdlfkalsdj
28 Jun 2007	leon button	ciao
22 May 2008	praveen kumar	These are really useful & essential programs.
01 Aug 2008	yuan qiangqiang	very good !
23 Oct 2008	Xuecang zhang	thanks a lot ,very convenient and powerful sharing is good
15 Oct 2011	LucasCritique	Fantastic package! Easy to use, stable, great documentation. Many thanks to the author!
07 Dec 2011	Martin Fuchs	Well written Code thanks to the Author
16 Dec 2011	ls	good work
23 Dec 2011	Piet	Great!

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Updates
	modifying description
05 Dec 2002	Added screenshot
25 Feb 2008	New version for Matlab 7.3, with a number of buf fixes and new capabilities, publihsed in Numer. Algo. 46, pp 189
18 Mar 2008	This minor update was necessary due to overlap of a function name (ilaplace) with the Symbolic Math Toolbox.

Tag Activity for this File
Tag	Applied By	Date/Time
linear algebra	Per Christian Hansen	22 Oct 2008 06:31:02
discrete	Per Christian Hansen	22 Oct 2008 06:31:02
illposed	Per Christian Hansen	22 Oct 2008 06:31:02
regularization	Per Christian Hansen	22 Oct 2008 06:31:02
mathematics	Per Christian Hansen	22 Oct 2008 06:31:02
discrete	trimm Oleksa	27 Apr 2009 08:15:50
illposed	trimm Oleksa	27 Apr 2009 08:15:54
regularization	trimm Oleksa	27 Apr 2009 08:15:56
discrete	Carlos	01 Aug 2010 17:56:32
discrete	Kai	31 Dec 2011 00:13:37

Highlights from regtools

regtools

Highlights from
regtools