L-curve Tikhonov
L-curve for Tikhonov regularization
l_curve_tikh_svd(U, s, d, npoints, varargin = NULL)
U |
matrix of data space basis vectors from the svd |
s |
vector of singular values |
d |
the data vector |
npoints |
the number of logarithmically spaced regularization parameters |
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 singular values |
Calculates the L-curve
eta |
the solution norm ||m|| or seminorm ||Lm|| |
rho |
the residual norm ||G m - d|| |
reg_param |
corresponding regularization parameters |
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$S
K1 = l_curve_tikh_svd(U1, diag(M1) , X1, 25, varargin = NULL)
rho1 =K1$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" ,
xlab="Residual Norm ||Gm-d||_2", ylab="Solution Seminorm ||Lm||_2" );Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.