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|
### sCorrect-updateMoment.R ---
##----------------------------------------------------------------------
## Author: Brice Ozenne
## Created: dec 10 2019 (09:58)
## Version:
## Last-Updated: jan 17 2022 (14:57)
## By: Brice Ozenne
## Update #: 232
##----------------------------------------------------------------------
##
### Commentary:
##
### Change Log:
##----------------------------------------------------------------------
##
### Code:
## * updateMoment
updateMoment <- function(skeleton, value, toUpdate,
name.pattern, unique.pattern,
param, Omega, endogenous, latent, n.cluster){
if(lava.options()$debug){cat("updateMoment \n")}
## remove attributes used by moments2
attr(Omega,"Omega.residuals") <- NULL
attr(Omega,"Omega.leverage") <- NULL
attr(Omega,"dOmega.leverage") <- NULL
n.endogenous <- length(endogenous)
n.latent <- length(latent)
## ** Update with the current values
name.update <- names(toUpdate[toUpdate==TRUE])
if(length(name.update)>0){
for(iUpdate in name.update){ ## iUpdate <- "Sigma"
if(iUpdate == "SigmaValue"){
index.update <- which(!is.na(skeleton$SigmaParam))
skeleton$SigmaValue[index.update] <- param[skeleton$SigmaParam[index.update]]
value$Sigma <- apply(skeleton$SigmaValue, MARGIN = 1:2, FUN = prod)
attr(value$Sigma,"detail") <- skeleton$SigmaValue
}else{
index.update <- which(!is.na(skeleton[[iUpdate]]))
value[[iUpdate]][index.update] <- param[skeleton[[iUpdate]][index.update]]
}
}
}
## ** Pre-compute relevant quantities
if(n.latent>0){
## alpha + X\Gamma
value$alpha.XGamma <- matrix(0, nrow = n.cluster, ncol = n.latent,
dimnames = list(NULL, latent))
if("alpha" %in% names(value)){
value$alpha.XGamma <- value$alpha.XGamma + skeleton$Xalpha %o% value$alpha
}
if("Gamma" %in% names(value)){
value$alpha.XGamma <- value$alpha.XGamma + do.call(cbind,lapply(latent, function(iL){skeleton$XGamma[[iL]] %*% value$Gamma[,iL]}))
}
## (I-B)^{-1}
if("B" %in% names(value)){
value$iIB <- solve(diag(1, nrow = n.latent, ncol = n.latent) - value$B)
}else{
value$iIB <- diag(1, nrow = n.latent, ncol = n.latent)
dimnames(value$iIB) <- list(latent,latent)
}
## (alpha + X\Gamma) (I-B)^{-1}
value$alpha.XGamma.iIB <- value$alpha.XGamma %*% value$iIB
## (I-B)^{-1} \Lambda
value$iIB.Lambda <- value$iIB %*% value$Lambda
value$tLambda.tiIB <- t(value$iIB.Lambda)
## \Psi (I-B)^{-1}
value$Psi.iIB <- value$Psi %*% value$iIB
## (I-B)^{-t} \Psi (I-B)^{-1}
value$tiIB.Psi.iIB <- t(value$iIB) %*% value$Psi
## \Lambda^t (I-B)^{-t} \Psi (I-B)^{-1}
value$tLambda.tiIB.Psi.iIB <- t(value$iIB.Lambda) %*% value$Psi.iIB
## (I-B)^{-t} \Psi (I-B)^{-1} \Lambda
value$tiIB.Psi.iIB.Lambda <- t(value$tLambda.tiIB.Psi.iIB)
}
## ** Compute mean
value$mu <- matrix(0, nrow = n.cluster, ncol = n.endogenous,
dimnames = list(NULL,endogenous))
if("nu" %in% names(value)){
value$mu <- value$mu + sweep(skeleton$Xnu, MARGIN = 2, FUN = "*", STATS = value$nu)
}
if("K" %in% names(value)){
value$mu <- value$mu + do.call(cbind,lapply(endogenous, function(iE){skeleton$XK[[iE]] %*% value$K[,iE]})) ## iE <- endogenous[1]
}
if(n.latent>0){
value$mu <- value$mu + value$alpha.XGamma %*% value$iIB.Lambda
}
## ** Compute variance
Omega.param <- matrix(0, nrow = n.endogenous, ncol = n.endogenous,
dimnames = list(endogenous,endogenous))
if("Sigma" %in% names(value)){
Omega.param <- Omega.param + value$Sigma
}
if("Psi" %in% names(value)){
Omega.param <- Omega.param + value$tLambda.tiIB.Psi.iIB %*% value$Lambda
}
if(!is.null(Omega)){
value$Omega <- Omega
attr(value$Omega,"discrepancy") <- Omega-Omega.param
}else{
value$Omega <- Omega.param
}
value$Omega.missing.pattern <- lapply(1:length(name.pattern), function(iM){ ## iM <- 1
iIndex <- which(unique.pattern[iM,]==1)
return(value$Omega[iIndex,iIndex,drop=FALSE])
})
names(value$Omega.missing.pattern) <- name.pattern
value$OmegaM1.missing.pattern <- lapply(value$Omega.missing.pattern, solve)
## ** Export
return(value)
}
## * updateDMoment
updateDMoment <- function(moment, skeleton, param){
if(lava.options()$debug){cat("updateDMoment \n")}
## ** import information
dmu <- skeleton$dmu.dparam
dOmega <- skeleton$dOmega.dparam
iIB.Lambda <- moment$iIB.Lambda
tLambda.tiIB <- moment$tLambda.tiIB
alpha.XGamma.iIB <- moment$alpha.XGamma.iIB
tiIB.Psi.iIB.Lambda <- moment$tiIB.Psi.iIB.Lambda
tLambda.tiIB.Psi.iIB <- moment$tLambda.tiIB.Psi.iIB
Sigma <- moment$Sigma
attr(Sigma,"detail") <- NULL
## ** Compute partial derivative regarding the mean
## NOTE: no "nu", "K", or "Gamma" as the partial derivative is independent of the parameter values
## and can therefore be computed once for all
if("alpha" %in% names(skeleton$dmat.dparam)){
iName.param <- names(skeleton$dmat.dparam$alpha)
for(iParam in iName.param){ ## iParam <- iName.param[1]
dmu[[iParam]] <- skeleton$dmat.dparam$alpha[[iParam]] %*% iIB.Lambda
}
}
if("Gamma" %in% names(skeleton$dmat.dparam)){
iName.param <- names(skeleton$dmat.dparam$Gamma)
for(iParam in iName.param){ ## iParam <- iName.param[1]
dmu[[iParam]] <- skeleton$dmat.dparam$Gamma[[iParam]] %*% iIB.Lambda
}
}
if("Lambda" %in% names(skeleton$dmat.dparam)){
iName.param <- names(skeleton$dmat.dparam$Lambda)
for(iParam in iName.param){ ## iParam <- iName.param[1]
dmu[[iParam]] <- alpha.XGamma.iIB %*% skeleton$dmat.dparam$Lambda[[iParam]]
}
}
if("B" %in% names(skeleton$dmat.dparam)){
iName.param <- names(skeleton$dmat.dparam$B)
for(iParam in iName.param){ ## iParam <- iName.param[1]
dmu[[iParam]] <- alpha.XGamma.iIB %*% skeleton$dmat.dparam$B[[iParam]] %*% iIB.Lambda
}
}
## ** Compute partial derivative regarding the variance
if("Lambda" %in% names(skeleton$dmat.dparam)){
iName.param <- names(skeleton$dmat.dparam$Lambda)
for(iParam in iName.param){ ## iParam <- iName.param[1]
dOmega[[iParam]] <- t(skeleton$dmat.dparam$Lambda[[iParam]]) %*% tiIB.Psi.iIB.Lambda + tLambda.tiIB.Psi.iIB %*% skeleton$dmat.dparam$Lambda[[iParam]]
}
}
if("B" %in% names(skeleton$dmat.dparam)){
iName.param <- names(skeleton$dmat.dparam$B)
for(iParam in iName.param){ ## iParam <- iName.param[1]
dOmega[[iParam]] <- t(iIB.Lambda) %*% t(skeleton$dmat.dparam$B[[iParam]]) %*% tiIB.Psi.iIB.Lambda + tLambda.tiIB.Psi.iIB %*% skeleton$dmat.dparam$B[[iParam]] %*% iIB.Lambda
}
}
if("Psi" %in% names(skeleton$dmat.dparam)){
iName.param <- names(skeleton$dmat.dparam$Psi)
for(iParam in iName.param){ ## iParam <- iName.param[1]
dOmega[[iParam]] <- tLambda.tiIB %*% skeleton$dmat.dparam$Psi[[iParam]] %*% iIB.Lambda
}
}
## *** Export
return(list(dmu = dmu, dOmega = dOmega))
}
## * updateD2Moment
updateD2Moment <- function(moment, skeleton, param){
if(lava.options()$debug){cat("updateD2Moment \n")}
## ** Import information
d2mu <- skeleton$d2mu.dparam
d2Omega <- skeleton$d2Omega.dparam
dalpha <- skeleton$dmat.dparam$alpha
dLambda <- skeleton$dmat.dparam$Lambda
dGamma <- skeleton$dmat.dparam$Gamma
dB <- skeleton$dmat.dparam$B
dPsi <- skeleton$dmat.dparam$Psi
Psi <- moment$Psi
Lambda <- moment$Lambda
iIB <- moment$iIB
Psi.iIB <- moment$Psi.iIB
iIB.Lambda <- moment$iIB.Lambda
tLambda.tiIB <- moment$tLambda.tiIB
alpha.XGamma.iIB <- moment$alpha.XGamma.iIB
tiIB.Psi.iIB <- moment$tiIB.Psi.iIB
tiIB.Psi.iIB.Lambda <- moment$tiIB.Psi.iIB.Lambda
tLambda.tiIB.Psi.iIB <- moment$tLambda.tiIB.Psi.iIB
grid.mean <- skeleton$grid.d2moment$mean
grid.var <- skeleton$grid.d2moment$var
names.grid.mean <- names(grid.mean)
names.grid.var <- names(grid.var)
## ** Compute partial derivative regarding the mean
## NOTE: no "nu", "K", or "Gamma" as the partial derivative is 0
if("alpha.B" %in% names.grid.mean){
for(iP in 1:NROW(grid.mean$alpha.B)){ # iP <- 1
iName1 <- grid.mean$alpha.B[iP,"alpha"]
iName2 <- grid.mean$alpha.B[iP,"B"]
d2mu[[iName1]][[iName2]] <- dalpha[[iName1]] %*% iIB %*% dB[[iName2]] %*% iIB.Lambda
}
}
if("alpha.Lambda" %in% names.grid.mean){
for(iP in 1:NROW(grid.mean$alpha.Lambda)){ # iP <- 1
iName1 <- grid.mean$alpha.Lambda[iP,"alpha"]
iName2 <- grid.mean$alpha.Lambda[iP,"Lambda"]
d2mu[[iName1]][[iName2]] <- dalpha[[iName1]] %*% iIB %*% dLambda[[iName2]]
}
}
if("Gamma.B" %in% names.grid.mean){
for(iP in 1:NROW(grid.mean$Gamma.B)){ # iP <- 1
iName1 <- grid.mean$Gamma.B[iP,"Gamma"]
iName2 <- grid.mean$Gamma.B[iP,"B"]
d2mu[[iName1]][[iName2]] <- dGamma[[iName1]] %*% iIB %*% dB[[iName2]] %*% iIB.Lambda
}
}
if("Gamma.Lambda" %in% names.grid.mean){
for(iP in 1:NROW(grid.mean$Gamma.Lambda)){ # iP <- 1
iName1 <- grid.mean$Gamma.Lambda[iP,"Gamma"]
iName2 <- grid.mean$Gamma.Lambda[iP,"Lambda"]
d2mu[[iName1]][[iName2]] <- dGamma[[iName1]] %*% iIB %*% dLambda[[iName2]]
}
}
if("Lambda.B" %in% names.grid.mean){
for(iP in 1:NROW(grid.mean$Lambda.B)){ # iP <- 1
iName1 <- grid.mean$Lambda.B[iP,"Lambda"]
iName2 <- grid.mean$Lambda.B[iP,"B"]
d2mu[[iName1]][[iName2]] <- alpha.XGamma.iIB %*% dB[[iName2]] %*% iIB %*% dLambda[[iName1]]
}
}
if("B.B" %in% names.grid.mean){
for(iP in 1:NROW(grid.mean$B.B)){ # iP <- 1
iName1 <- grid.mean$B.B[iP,"B1"]
iName2 <- grid.mean$B.B[iP,"B2"]
term1 <- alpha.XGamma.iIB %*% dB[[iName2]] %*% iIB %*% dB[[iName1]] %*% iIB.Lambda
term2 <- alpha.XGamma.iIB %*% dB[[iName1]] %*% iIB %*% dB[[iName2]] %*% iIB.Lambda
d2mu[[iName1]][[iName2]] <- term1 + term2
}
}
## ** Compute partial derivative regarding the variance
if("Psi.Lambda" %in% names.grid.var){
for(iP in 1:NROW(grid.var$Psi.Lambda)){ # iP <- 1
iName1 <- grid.var$Psi.Lambda[iP,"Psi"]
iName2 <- grid.var$Psi.Lambda[iP,"Lambda"]
term1 <- t(dLambda[[iName2]]) %*% t(iIB) %*% dPsi[[iName1]] %*% iIB.Lambda
d2Omega[[iName1]][[iName2]] <- term1 + t(term1)
}
}
if("Psi.B" %in% names.grid.var){
for(iP in 1:NROW(grid.var$Psi.B)){ # iP <- 1
iName1 <- grid.var$Psi.B[iP,"Psi"]
iName2 <- grid.var$Psi.B[iP,"B"]
term1 <- t(iIB.Lambda) %*% t(dB[[iName2]]) %*% t(iIB) %*% dPsi[[iName1]] %*% iIB.Lambda
d2Omega[[iName1]][[iName2]] <- term1 + t(term1)
}
}
if("Lambda.B" %in% names.grid.var){
for(iP in 1:NROW(grid.var$Lambda.B)){ # iP <- 1
iName1 <- grid.var$Lambda.B[iP,"Lambda"]
iName2 <- grid.var$Lambda.B[iP,"B"]
term1 <- t(dLambda[[iName1]]) %*% t(iIB) %*% t(dB[[iName2]]) %*% t(iIB) %*% Psi %*% iIB.Lambda
term2 <- t(dLambda[[iName1]]) %*% t(iIB) %*% Psi %*% iIB %*% dB[[iName2]] %*% iIB.Lambda
## term2 <- tLambda.tiIB.Psi.iIB %*% dB[[iName2]] %*% iIB %*% dLambda[[iName1]]
d2Omega[[iName1]][[iName2]] <- term1 + t(term1) + term2 + t(term2)
}
}
if("Lambda.Lambda" %in% names.grid.var){
for(iP in 1:NROW(grid.var$Lambda.Lambda)){ # iP <- 1
iName1 <- grid.var$Lambda.Lambda[iP,"Lambda1"]
iName2 <- grid.var$Lambda.Lambda[iP,"Lambda2"]
term1 <- t(dLambda[[iName1]]) %*% t(iIB) %*% Psi.iIB %*% dLambda[[iName2]]
d2Omega[[iName1]][[iName2]] <- term1 + t(term1)
}
}
if("B.B" %in% names.grid.var){
for(iP in 1:NROW(grid.var$B.B)){ # iP <- 1
iName1 <- grid.var$B.B[iP,"B1"]
iName2 <- grid.var$B.B[iP,"B2"]
term1 <- t(iIB.Lambda) %*% t(dB[[iName2]]) %*% t(iIB) %*% t(dB[[iName1]]) %*% t(iIB) %*% Psi.iIB %*% Lambda
term2 <- t(iIB.Lambda) %*% t(dB[[iName1]]) %*% t(iIB) %*% t(dB[[iName2]]) %*% t(iIB) %*% Psi.iIB %*% Lambda
term3 <- t(iIB.Lambda) %*% t(dB[[iName1]]) %*% t(iIB) %*% Psi.iIB %*% dB[[iName2]] %*% iIB %*% Lambda
d2Omega[[iName1]][[iName2]] <- term1 + t(term1) + term2 + t(term2) + term3 + t(term3)
}
}
## ** Export
return(list(d2mu = d2mu, d2Omega = d2Omega))
}
######################################################################
### sCorrect-updateMoment.R ends here
|
