multiband (version 0.1.0)

update_amplitude: Update Amplitude parameter

Description

update_amplitude solves a simple linear system of equations (rank 1 perturbation on a diagonal matrix) to update the amplitude estimates.

Usage

update_amplitude(tms, beta, rho, omega, at, gamma)

Arguments

tms

list of matrices whose rows are the triple (t,mu,sigma) for each band

beta

vector of the current intercept estimates

rho

vector of the current phase estimates

omega

frequency

at

prior vector

gamma

nonnegative regularization parameter

Examples

test_data <- synthetic_multiband()
B <- test_data$B
tms <- test_data$tms
beta <- test_data$beta
rho <- test_data$rho
omega <- test_data$omega
gamma <- 1
at <- rnorm(B)
at <- as.matrix(at/sqrt(sum(at**2)),ncol=1)

## Check answer
a_next <- update_amplitude(tms,beta,rho,omega,at,gamma)

e <- double(B)
xi <- double(B)
for (b in 1:B) {
  nb <- length(tms[[b]][,1])
  s <- sin(omega*tms[[b]][,1] + rho[b])
  w <- 1/(tms[[b]][,3]**2)
  e[b] <- t(s)%*%(w*s) + gamma
  xi[b] <- t(s)%*%(w*(tms[[b]][,2]-beta[b]))
}
a_direct <- solve(diag(e)-gamma*at%*%t(at),xi)
norm(as.matrix(a_direct-a_next),'f')