L-curve tikh gsvd
L-curve tikh gsvd
l_curve_tikh_gsvd(U, d, X, Lam, Mu, G, L, npoints, varargin = NULL)
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 |
|
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 |
Uses output of GSVD
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>
#### 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" );Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.