update_amplitude: Update Amplitude parameter

In multiband: Period Estimation for Multiple Bands

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')

multiband documentation built on May 2, 2019, 3:30 a.m.