Nothing
####
#### Routines for hyperplane inflation simulation technique
#### (see Petris & Tardella)
####
lpi <- log(base::pi)
lsqPi <- log(sqrt(base::pi))
rballunif <- function(n, d) {
## generate a point uniformly in the n-dimensional ball
## centered at the origin and having radius `d'
x <- rnorm(n)
d * runif(1)^(1/n) * x / sqrt(crossprod(x))
}
"trans.dens" <-
function(y, ldens.list, which.models, ..., back.transform=F) {
## y can be a vector
## or a n by p matrix, whose rows are the points at which
## to evaluate trans.dens
## ldens.list is a list of logdensities
## which.models is a sequence of model indices
## For each point of `y', the function returns one of the following:
## 1) if back.transform=F only the _log_ of the transformed density
## 2) if back.transform=T a vector of
## (n+2) elements where
## *the first one, named "trans.dens",
## is the _log_ of the transformed density
## **the second one, named "model.index",
## is the corresponding submodel region
## ***the last n elements represent the corresponding
## x vector in the original submodel space
# if ( is.null(ldens.list) )
# stop("ldens.list empty")
# if ( any(diff(which.models) <= 0) )
# stop("model indices must be given in increasing order")
if ( which.models[1] != 0 )
which.models <- c(0, which.models)
# if ( length(which.models) != length(ldens.list) )
# stop("ldens.list and which.models must have the same length")
if ( !is.matrix(y) )
y <- t(as.matrix(y))
n.points <- nrow(y)
n <- ncol(y)
ans <- matrix( 0, n.points, 2+n )
## n=dimension of the largest embedding space
## ??? shouldn't it be compatible with (that is the same as)
## which.models[length(wihich.models)] ????
## add a new check ???
for ( loop in 1:n.points ) {
z <- y[loop,]
i <- length( which.models )
h <- n - ( k <- which.models[i] )
if ( h == 0 ){
logd <- -( ldens.list[[1]](rep(0,n),...) + (n/2)*lpi -
(( ldens.list[[i]](...) + lgamma(k/2+1)) ))/k
}
else{
logd <- -( ldens.list[[1]]( c(z[1:h], rep(0,k)), ... ) + (k/2)*lpi -
(( ldens.list[[i]](z[1:h],...) + lgamma(k/2+1))) )/k
}
## rewrite the if below in a more efficient way...?
if ( ( h == 0 && log(sum(z^2)) > 2*logd ) || ( h > 0 && log(sum(z[-(1:h)]^2)) > 2*logd ) ) {
if ( h == 0 ){
z <- ldeflate( z, logd )
}
else{
z[-(1:h)] <- ldeflate( z[-(1:h)], logd )
}
i <- i - 1
h <- n - ( k <- which.models[i] )
if ( i > 1 ) {
logd <- -(( ldens.list[[1]]( c(z[1:h], rep(0,k)), ... )+(k/2)*lpi) -
(( ldens.list[[i]](z[1:h],...) + lgamma(k/2+1)) ))/k
while ( (i > 1) && (log(sum(z[-(1:h)]^2)) > (2*logd) )) {
z[-(1:h)] <- ldeflate( z[-(1:h)], logd )
i <- i - 1
h <- n - ( k <- which.models[i] )
if ( k > 0 ) {
logd <- -( ldens.list[[1]]( c(z[1:h], rep(0,k)), ... ) + (k/2)*lpi -
(( ldens.list[[i]](z[1:h],...) + lgamma(k/2+1)) ))/k
c(z[1:h], rep(0,k)) }
}
}
}
if ( k == n )
x <- rep(0,k)
else
x <- c( z[1:h], rep(0,k) )
ans[loop,] <- c(ldens.list[[1]](x,...), k, x )
}
if ( back.transform ) {
dimnames(ans) <- list(NULL,c("trans.dens", "model.index", paste("x",1:n,sep=".")))
return(ans)
}
else
return(ans[,1])
}
linflate <- function(y, logh) {
norm.y <- sqrt( y %*% y )
n <- length(y)
y * ( norm.y^n + exp(n*logh) )^(1/n) / norm.y
}
ldeflate <- function(y, logh) {
norm.y <- sqrt( y %*% y )
n <- length(y)
y * ( norm.y^n - exp(n*logh) )^(1/n) / norm.y
}
"trans.up" <-
function(x, ldens.list, which.models, ...) {
## aim: it maps back a point in the "original model scale"
## to an appropriate point in the "inflated scale"
## corresponding to the same submodel subspace
## x can be a vector or a n by p matrix,
## whose rows are the points to be transformed
## ldens.list is a list of densities
## which.models is a sequence of model indices
# if ( is.null(ldens.list) )
# stop("ldens.list empty")
# if ( any(diff(which.models) <= 0) )
# stop("model indices must be given in increasing order")
if ( which.models[1] != 0 )
which.models <- c(0, which.models)
# if ( length(which.models) != length(ldens.list) )
# stop("ldens.list and which.models must have the same length")
if ( !is.matrix(x) )
x <- t(as.matrix(x))
n.points <- nrow(x)
n <- ncol(x)
ans <- matrix( 0, n.points, n )
for ( loop in 1:n.points ) {
z <- x[loop,]
k <- 0
while ( (z[n-k] == 0) && (k < n) ) k <- k+1
if ( k > 0 ) # some components are zero
if ( length(j <- which( which.models == k )) > 0 ) {
m <- n-k
if ( m == 0 ) {
logd <- ( ldens.list[[j]](...) - ldens.list[[1]]( rep(0,k), ... ) +
lgamma(k/2+1) ) / k - 0.5*lpi
z <- rballunif( k, exp(logd) )
}
else {
logd <- ( ldens.list[[j]](z[1:m],...) -
ldens.list[[1]]( c(z[1:m], rep(0,k)), ... ) +
lgamma(k/2+1) ) / k - 0.5*lpi
z[-(1:m)] <- rballunif( k, exp(logd) )
}
}
if ( k < n ) { # not all the components are zero
for ( i in (k+1):n )
if ( length(j <- which( which.models == i )) > 0 ) {
m <- n-i
if ( m == 0 ) {
logd <- ( ldens.list[[j]](...) - ldens.list[[1]]( rep(0,i), ... ) +
lgamma(i/2+1) ) / i - 0.5*lpi
z <- linflate( z, logd )
}
else {
logd <- ( ldens.list[[j]](z[1:m],...) -
ldens.list[[1]]( c(z[1:m], rep(0,i)), ... ) +
lgamma(i/2+1) ) / i - 0.5*lpi
z[-(1:m)] <- linflate( z[-(1:m)], logd )
}
}
}
ans[loop,] <- z
}
return(ans)
}
### transformed log density for the mixture of two components
"trans2" <-
function(y, ldens.list, k, ...) {
## 'y' is a vector
## returns also the model index of the vector 'y'
if (length(ldens.list) != 2 || length(k) != 1)
stop("ldens.list must have length 2\nand k must have length 1")
n <- length(y)
h <- n - k # dimension of submodel 'k'
if (h==0)
{
ldk <- ldens.list[[2]](...)
if ( is.infinite(ldk) && ldk < 0 )
return(c(ldens.list[[1]](y,...), 0))
ld0 <- ldens.list[[1]](rep(0,n),...)
}
else
{
ldk <- ldens.list[[2]](y[1:h],...)
if ( is.infinite(ldk) && ldk < 0 )
return(c(ldens.list[[1]](y,...), 0))
ld0 <- ldens.list[[1]](c(y[1:h],rep(0,k)),...)
}
if ( is.infinite(ld0) && ld0 < 0 )
stop(paste("ldens.list[[1]] may not take the value",ld0))
u <- ldk - ld0 + lgamma(k/2 + 1) - k*lsqPi -
0.5 * k * log(crossprod(y[(n-k+1):n]))
if ( u > 0 )
return(c(ld0, k))
else
return(c(ldens.list[[1]](y * rep(c(1,(1-exp(u))^(1/k)),c(h,k)),...), 0))
}
### Map points in the auxiliary space back to the original one
"transBack2" <-
function(y, ldens.list, k, ...) {
## 'y' is a vector or a matrix
## back.transform not implemented yet
## returns also the model index of the vector 'y'
if (length(ldens.list) != 2 || length(k) != 1)
stop("ldens.list must have length 2\nand k must have length 1")
if ( !is.null(dim(y)) )
{
ans <- matrix(0,NROW(y),NCOL(y))
for (i in 1:NROW(ans))
ans[i,] <- Recall(y[i,], ldens.list, k, ...)
return(ans)
}
n <- length(y)
h <- n - k # dimension of submodel 'k'
if (h==0)
{
ldk <- ldens.list[[2]](...)
if ( is.infinite(ldk) && ldk < 0 )
return(y)
z <- rep(0,n)
}
else
{
ldk <- ldens.list[[2]](y[1:h],...)
if ( is.infinite(ldk) && ldk < 0 )
return(y)
z <- c(y[1:h],rep(0,k))
}
ld0 <- ldens.list[[1]](z, ...)
if ( is.infinite(ld0) && ld0 < 0 )
stop(paste("ldens.list[[1]] may not take the value",ld0))
u <- ldk - ld0 + lgamma(k/2 + 1) - k*lsqPi -
0.5 * k * log(crossprod(y[(n-k+1):n]))
if ( u > 0 )
return(z)
else
return(y * rep(c(1,(1-exp(u))^(1/k)),c(h,k)))
}
"transUp2" <-
function(y, ldens.list, k, ...) {
## 'y' is a vector
n <- length(y)
h <- n - k # dimension of submodel 'k'
ind.h <- seq(1,length.out=h)
if (h==0)
{
ldk <- ldens.list[[2]](...)
if ( is.infinite(ldk) && ldk < 0 ) return(y)
ld0 <- ldens.list[[1]](rep(0,n),...)
}
else
{
ldk <- ldens.list[[2]](y[ind.h],...)
if ( is.infinite(ldk) && ldk < 0 ) return(y)
ld0 <- ldens.list[[1]](c(y[ind.h],rep(0,k)),...)
}
if ( is.infinite(ld0) && ld0 < 0 )
stop(paste("ldens.list[[1]] may not take the value",ld0))
r <- ldk - ld0 + lgamma(k/2 + 1) - k*lsqPi
u <- r - 0.5 * k * log(crossprod(y[(n-k+1):n]))
if ( u > 0 )
{
## model 'k'
return( c(y[ind.h], rballunif(k,exp(r/k))) )
}
else
{
## model '0'
return( y * rep(c(1,(1-exp(u))^(1/k)),c(h,k)) )
}
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.