L curve tgsvd
L curve parematers and models for truncated gsvd regularization.
l_curve_tgsvd(U, d, X, Lam, G, L)
U |
U, output of GSVD |
d |
output of GSVD |
X |
output of GSVD |
Lam |
output of GSVD |
G |
output of GSVD |
L |
output of GSVD |
List:
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 |
Jonathan M. Lees<jonathan.lees@unc.edu>
Aster, R.C., C.H. Thurber, and B. Borchers, Parameter Estimation and Inverse Problems, Elsevier Academic Press, Amsterdam, 2005.
#### 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$S
K1 = l_curve_tgsvd(U1,t,X1,Lam1,G,L1);
rho1 =K1$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" );Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.