l_curve_tikh_gsvd: L-curve tikh gsvd

In PEIP: Geophysical Inverse Theory and Optimization

L-curve tikh gsvd

Description

L-curve tikh gsvd

Usage

l_curve_tikh_gsvd(U, d, X, Lam, Mu, G, L, npoints, varargin = NULL)

Arguments

U	from the gsvd
d	data vector for the problem G*m=d
X	from the gsvd
Lam	from the gsvd
Mu	from the gsvd
G	system matrix
L	roughening matrix
npoints	Number of points
varargin	alpha_min, alpha_max: if specified, constrain the logrithmically spaced regularization parameter range, otherwise an attempt is made to estimate them from the range of generalized singular values

Details

Uses output of GSVD

Value

eta	- the solution seminorm ||Lm||
rho	- the residual norm ||G m - d||
reg_param	- corresponding regularization parameters
m	- corresponding suite of models for truncated GSVD

Author(s)

Jonathan M. Lees<[e-mail]>

Examples

####  Vertical Seismic Profile example
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

K1 =  l_curve_tikh_gsvd(U1,t,X1,Lam1,M1, G,L1, 25);

rho1 =K1$rho
eta1 =K1$eta
reg_param1 =K1$reg_param
m1s =K1$m


###  store where the corner is (from visual inspection)
ireg_corner1=8;
rho_corner1=rho1[ireg_corner1];
eta_corner1=eta1[ireg_corner1];
print(paste('1st order reg corner is:  ',ireg_corner1));


plot(rho1,eta1,type="b", log="xy", xlim=c(1e-4, 1e-2) , ylim=c(6e-6, 2e-4) ,
     xlab="Residual Norm ||Gm-d||_2", ylab="Solution Seminorm ||Lm||_2"  );

 

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