R/computation-armsSampler.R

In mmeta: Multivariate Meta-Analysis

#####################################################################################################################################################
####  Copy from the R package HI: Simulation from distributions supported by nested hyperplanes because this package has been removed from CRAN
###Simulation from distributions supported by nested hyperplanes, using the algorithm described in Petris & Tardella, "A geometric approach to transdimensional Markov chain Monte Carlo", Canadian Journal of Statistics, v.31, n.4, (2003). Also random direction multivariate Adaptive Rejection Metropolis Sampling.
###Version: 0.4
###Author: Giovanni Petris and Luca Tardella; original C code for ARMS by Wally Gilks.
#Maintainer: Giovanni Petris <GPetris at Uark.edu>
#######################################################################################################################################################



### To find the boundary of a bounded convex set
convex.bounds <-function (x, dir, indFunc, ..., tol = 1e-07) 
{
  ###########################################################
  ## x: a point within the set
  ## dir: a vector giving the direction along which bounds are sought
  ## indFunc: the indicator function of a bounded convex set
  ## ... : additional arguments passed to indFunc
  ############################################################
  if (all(dir == 0)) 
    stop("invalid direction in convex.bounds()")
  if (indFunc(x, ...) < 0.5) 
    stop("x not in the support of indFunc")
  f.onedim <- function(u) indFunc(x + u * dir, ...)
  e <- -2
  while (f.onedim(e) > 0.5) e <- e * 2
  lower <- e
  e <- 2
  while (f.onedim(e) > 0.5) e <- e * 2
  upper <- e
  ans <- numeric(2)
  ## search for `lower' boundary along dir
  bracket.low <- lower
  bracket.high <- 0
  repeat {
    cand <- 0.5 * (bracket.low + bracket.high)
    if (f.onedim(cand) > 0.5) 
      bracket.high <- cand
    else bracket.low <- cand
    if (bracket.high - bracket.low < tol) {
      ans[1] <- bracket.high
      break
    }
  }
  ## search for `upper' boundary along dir
  bracket.low <- 0
  bracket.high <- upper
  repeat {
    cand <- 0.5 * (bracket.low + bracket.high)
    if (f.onedim(cand) > 0.5) 
      bracket.low <- cand
    else bracket.high <- cand
    if (bracket.high - bracket.low < tol) {
      ans[2] <- bracket.low
      break
    }
  }
  return(ans)
}

### Wrapper to arms.c
arms <-function (y.start, myldens, indFunc, n.sample, ...) 
{
  if(.Platform$OS.type=="unix")
    path<-file.path(find.package("mmeta"),"libs","mmeta.so")
  
  if(.Platform$OS.type=="windows"){
    if(.Platform$r_arch=="i386") path<-file.path(find.package("mmeta"),"libs","i386","mmeta.dll")
    if(.Platform$r_arch=="x64")  path<-file.path(find.package("mmeta"),"libs","x64","mmeta.dll")
    
  }
  dyn.load(path)
  ## y.start: starting point
  ## myldens: univariate or multivariate logdensity from which a sample
  ##          needs to be generated
  ## indFunc: the indicator function of the support of myldens
  ##          (assumed to be convex and bounded)
  ## n.sample: desired sample size
  ## ...     : additional arguments passed to myldens and indFunc
  ## sanity checks first
  #     if (mode(myldens) != "function") 
  #         stop("myldens not a function")
  #     if (mode(indFunc) != "function") 
  #         stop("indFunc not a function")
  #     if (n.sample < 0) 
  #         stop("n.sample must be nonnegative")
  #     if (n.sample < 1) 
  #         return(numeric(0))
  #     if (!is.numeric(y.start)) 
  #         stop("non numeric argument y.start")
  dim <- length(y.start)
  #     if (dim == 0) 
  #         stop("starting point has length zero")
  #     if (!(indFunc(y.start, ...) > 0)) 
  #         stop("starting point not in the support")
  if (dim == 1) {
    bounds <- y.start + convex.bounds(y.start, dir = 1, indFunc, 
                                      ...)
    if ( diff(bounds) < 1e-7 )
      y.sample <- rep(y.start, n.sample)
    else {
      f <- function(x) myldens(x, ...)
      y.sample <- .Call("arms", bounds, f, y.start, as.integer(n.sample), 
                        new.env(),PACKAGE="mmeta")
    }
  }
  else {
    y.sample <- rbind(y.start, matrix(0, n.sample, dim))
    for (k in 1:n.sample) {
      ## pick a direction at random 
      dir <- rnorm(dim)
      ## look for boundaries of support in the selected direction
      bounds <- convex.bounds(y.sample[k, ], dir, indFunc, 
                              ...)
      if ( diff(bounds) < 1e-7 )
        y.sample[k + 1, ] <- y.sample[k, ]
      else {
        ## define the univariate density to be passed to arms.c
        f <- function(x) myldens(y.sample[k, ] + x * dir, 
                                 ...)
        ## call arms.c
        y.sample[k + 1, ] <- y.sample[k, ] + dir * .Call("arms", 
                                                         bounds, f, 0, as.integer(1), new.env(),PACKAGE="mmeta")
      }
    }
    y.sample <- y.sample[-1, ]
  }
  return(y.sample)
}



####
#### 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)) )
      
    }
  }