Picard plot
Picard plot parameters for subsequent plotting.
picard_vals(U, sm, d)
U |
the U matrix from the SVD or GSVD |
sm |
singular values in decreasing order, or the GSVD lambdas divided by the mus in decreasing order |
d |
data to fit, right hand side |
The Picard plot is a method of helping to determine regularization schemes.
List:
utd |
the columns of U transposed times d |
utd_norm |
utd./sm |
Jonathan M. Lees<jonathan.lees@unc.edu>
GSVD
####
n = 20
G = shawG(n,n)
spike = rep(0,n)
spike[10] = 1
dspiken = G
set.seed(2015)
dspiken = dspiken + 6e-6 *rnorm(length(dspiken))
Utube=svd(G);
U = Utube$u
V = Utube$v
S = Utube$d
s=Utube$d
R3 = picard_vals(U,s,dspiken);
utd = R3$utd
utd_norm= R3$utd_norm
### Produce the Picard plot.
x_ind=1:length(s);
##
plot( range(x_ind) , range(c(s ,abs(utd),abs(utd_norm))),
type='n', log='y', xlab="i", ylab="" )
lines(x_ind,s, col='black')
points(x_ind,abs(utd), pch=1, col='red')
points(x_ind,abs(utd_norm), pch=2, col='blue')
title("Picard Plot for Shaw Problem")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.