gcval: Get c-val

In PEIP: Geophysical Inverse Theory and Optimization

Get c-val

Description

Extract the smallest regularization parameter.

Usage

gcval(U, s, b, npoints)

Arguments

U	U matrix from gsvd(G, L)
s	[diag(C) diag(S)] which are the lambdas and mus from the gsvd
b	the data to try and match
npoints	number of alphas to estimate

Details

Evaluate the GCV function gcv_function at npoints points.

Value

List:

reg_min	alpha with the minimal g (scalar)
g	|| Gm_(alpha,L) - d ||^2 / (Tr(I - GG#)^2
alpha	alpha for the corresponding g

Author(s)

Jonathan M. Lees<[e-mail]>

See Also

gcv_function

Examples

set.seed(2015)
VSP = vspprofile()
t = VSP$t2
G = VSP$G
M = VSP$M
N = VSP$N

L1 = get_l_rough(N,1);
littleU = PEIP::GSVD(as.matrix(G), as.matrix(L1) );

BIGU = flipGSVD(littleU, dim(G), dim(L1) )

U1 = BIGU$U
V1 =BIGU$V
X1=BIGU$X
Lam1=BIGU$C
M1=BIGU$S

lam=sqrt(diag(t(Lam1 %*% Lam1)));

mu=sqrt(diag(t(M1)%*%M1));

p=rnk(L1);

sm1=cbind(lam[1:p],mu[1:p])

### % get the gcv values varying alpha

###
ngcvpoints=1000;

HI = gcval(U1,sm1,t,ngcvpoints);

PEIP documentation built on Aug. 21, 2023, 9:10 a.m.