L Curve Corner
Retrieve corner of L-curve
l_curve_corner(rho, eta, reg_param)
rho |
misfit |
eta |
model norm or seminorm |
reg_param |
regularization parameter |
reg_corner |
the value of reg_param with maximum curvature |
ireg_corner |
the index of the value in reg_param with maximum curvature |
kappa |
the curvature for each reg_param |
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$m
### % store where the corner is (from visual inspection)
vcorn = l_curve_corner(rho1, eta1, reg_param1)
ireg_corner1=vcorn$reg_corner
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" );
points(rho_corner1, eta_corner1, col='red', cex=2 )Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.