L Curve Corner

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Description

Retrieve corner of L-curve

Usage

1
l_curve_corner(rho, eta, reg_param)

Arguments

rho

misfit

eta

model norm or seminorm

reg_param

regularization parameter

Value

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

Author(s)

Jonathan M. Lees<jonathan.lees@unc.edu>

References

Aster, R.C., C.H. Thurber, and B. Borchers, Parameter Estimation and Inverse Problems, Elsevier Academic Press, Amsterdam, 2005.

Examples

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####  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 )

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