picard_vals: Picard plot

In PEIP: Geophysical Inverse Theory and Optimization

Picard plot

Description

Picard plot parameters for subsequent plotting.

Usage

picard_vals(U, sm, d)

Arguments

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

Details

The Picard plot is a method of helping to determine regularization schemes.

Value

List:

utd	the columns of U transposed times d
utd_norm	utd./sm

Author(s)

Jonathan M. Lees<[e-mail]>

See Also

GSVD

Examples

####
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")

PEIP documentation built on Aug. 21, 2023, 9:10 a.m.