regtools: gcvfun(lambda,s2,beta,delta0,mn,dsvd) - File Exchange

Code covered by the BSD License

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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from regtools by Per Christian Hansen
Analysis and Solution of Discrete Ill-Posed Problems.

gcvfun(lambda,s2,beta,delta0,mn,dsvd)

function G = gcvfun(lambda,s2,beta,delta0,mn,dsvd)

% Auxiliary routine for gcv.  PCH, IMM, Feb. 24, 2008.

% Note: f = 1 - filter-factors.
if (nargin==5)
   f = (lambda^2)./(s2 + lambda^2);
else
   f = lambda./(s2 + lambda);
end
G = (norm(f.*beta)^2 + delta0)/(mn + sum(f))^2;

Highlights from regtools

Highlights from
regtools