R/sigex.eta2psi.r

In jlivsey/sigex: Ecce Signum: Multivariate Signal Extraction

#' 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
#'
#' @param eta free variables of real numbers.  Must have length given by
#'     dim(constraint.mat)[2] - dim(constraint.mat)[1]
#' @param	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.
#'
#' @return psi: a vector of all the real hyper-parameters.
#' @export
#'

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)
}