sigex.eta2psi <- function(eta,constraint)
{
##########################################################################
#
# sigex.eta2psi
# Copyright (C) 2019 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: transform eta to psi
# Background:
# psi refers to a vector of real numbers containing all
# hyper-parameters (i.e., reals mapped bijectively to the parameter
# manifold), whereas eta consists of free variables of real numbers
# that are mapped to a fixed set nu, and psi is a permuted
# vector of eta and nu.
# Notes: this is a functional inverse to sigex.psi2eta
# Inputs:
# eta: see background. Must have length given by
# dim(constraint.mat)[2] - dim(constraint.mat)[1]
# constraint: matrix of the form [Q , C], with C (constraint.mat)
# the matrix of constraints and Q (constraint.vec) the vector
# of constraint constants, such that C psi = Q.
# Outputs:
# psi: see background.
#
####################################################################
psi <- eta
if(length(constraint) > 0)
{
constraint.mat <- constraint[,-1,drop=FALSE]
constraint.vec <- constraint[,1,drop=FALSE]
## compute decomposition
constraint.qr <- qr(constraint.mat)
constraint.q <- qr.Q(constraint.qr)
constraint.r <- qr.R(constraint.qr)
constraint.pivot <- constraint.qr$pivot
constraint.ipivot <- sort.list(constraint.pivot)
## compute mapping from free variables
fixed.dim <- dim(constraint.mat)[1]
free.dim <- dim(constraint.mat)[2] - fixed.dim
trans.mat <- solve(constraint.r[,1:fixed.dim,drop=FALSE],
constraint.r[,(fixed.dim+1):(fixed.dim+free.dim),drop=FALSE])
trans.vec <- solve(constraint.r[,1:fixed.dim,drop=FALSE]) %*% solve(constraint.q) %*% constraint.vec
nu <- trans.vec - trans.mat %*% eta
psi <- c(nu,eta)[constraint.ipivot]
}
return(psi)
}
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