sigex.conditions <- function(data.ts,psi,mdl)
{
##########################################################################
#
# sigex.conditions
# Copyright (C) 2017 Tucker McElroy
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
#
############################################################################
################# Documentation #####################################
#
# Purpose: computes condition number for a covariance matrix
# Background: a non-negative definite matrix Sigma has a
# Generalized Cholesky Decomposition (GCD) of the form
# Sigma = L %*% D %*% t(L),
# where L is unit lower triangular and D is diagonal with
# non-negative entries, referred to as the Schur complements
# of Sigma. The number of nonzero Schur complements equals
# the rank of Sigma. The condition numbers can be computed
# by dividing D by the diagonal of Sigma.
# param is the name for the model parameters entered into
# a list object with a more intuitive structure, whereas
# psi refers to a vector of real numbers containing all
# hyper-parameters (i.e., reals mapped bijectively to the parameter manifold)
# Inputs:
# data.ts: a T x N matrix ts object
# psi: see background.
# mdl: the specified sigex model, a list object
# Outputs:
# conds: a S x N matrix of condition numbers, where
# S is the number of components. Each row gives
# the N condition numbers for the innovation
# covariance matrix of the corresponding latent component.
# Requires: sigex.param2gcd, getGCD
#
####################################################################
x <- t(data.ts)
N <- dim(x)[1]
T <- dim(x)[2]
# get xi portion
ind <- 0
A.mat <- matrix(0,N,N)
A.mat[lower.tri(A.mat)] <- 1
conds <- NULL
for(i in 1:length(mdl[[3]]))
{
vrank <- mdl[[1]][[i]]
D.dim <- length(vrank)
L.dim <- sum(A.mat[,as.vector(vrank)])
L.psi <- NULL
if(L.dim > 0) L.psi <- psi[(ind+1):(ind+L.dim)]
ind <- ind+L.dim
D.psi <- psi[(ind+1):(ind+D.dim)]
ind <- ind+D.dim
L.mat <- sigex.param2gcd(L.psi,N,as.vector(vrank))
k.order <- length(D.psi)
cov.mat <- L.mat %*% diag(exp(D.psi),nrow=k.order) %*% t(L.mat)
eta2 <- getGCD(cov.mat,N)[[2]]/diag(cov.mat)
eta2[diag(cov.mat)==0] <- 0
eta2[1] <- 1
conds <- rbind(conds,eta2)
}
return(conds)
}
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