[epclust.git] / epclust / R / clustering.R

#' @name clustering
#' @rdname clustering
#' @aliases clusteringTask1 computeClusters1 computeClusters2
#'
#' @title Two-stage clustering, withing one task (see \code{claws()})
#'
#' @description \code{clusteringTask1()} runs one full stage-1 task, which consists in
#'   iterated stage 1 clustering (on nb_curves / ntasks energy contributions, computed
#'   through discrete wavelets coefficients). \code{computeClusters1()} and
#'   \code{computeClusters2()} correspond to the atomic clustering procedures respectively
#'   for stage 1 and 2. The former applies the clustering algorithm (PAM) on a
#'   contributions matrix, while the latter clusters a chunk of series inside one task
#'   (~max nb_series_per_chunk)
#'
#' @param indices Range of series indices to cluster in parallel (initial data)
#' @param getContribs Function to retrieve contributions from initial series indices:
#'   \code{getContribs(indices)} outpus a contributions matrix
#' @param contribs matrix of contributions (e.g. output of \code{curvesToContribs()})
#' @inheritParams computeSynchrones
#' @inheritParams claws
#'
#' @return For \code{clusteringTask1()} and \code{computeClusters1()}, the indices of the
#'   computed (K1) medoids. Indices are irrelevant for stage 2 clustering, thus
#'   \code{computeClusters2()} outputs a big.matrix of medoids
#'   (of size limited by nb_series_per_chunk)
NULL

#' @rdname clustering
#' @export
clusteringTask1 = function(
	indices, getContribs, K1, nb_series_per_chunk, ncores_clust=1, verbose=FALSE, parll=TRUE)
{
	if (verbose)
		cat(paste("*** Clustering task on ",length(indices)," lines\n", sep=""))

	wrapComputeClusters1 = function(inds) {
		if (parll)
			require("epclust", quietly=TRUE)
		if (verbose)
			cat(paste("   computeClusters1() on ",length(inds)," lines\n", sep=""))
		inds[ computeClusters1(getContribs(inds), K1) ]
	}

	if (parll)
	{
		cl = parallel::makeCluster(ncores_clust)
		parallel::clusterExport(cl, varlist=c("getContribs","K1","verbose"), envir=environment())
	}
	while (length(indices) > K1)
	{
		indices_workers = .spreadIndices(indices, nb_series_per_chunk)
		if (parll)
			indices = unlist( parallel::parLapply(cl, indices_workers, wrapComputeClusters1) )
		else
			indices = unlist( lapply(indices_workers, wrapComputeClusters1) )
	}
	if (parll)
		parallel::stopCluster(cl)

	indices #medoids
}

#' @rdname clustering
#' @export
computeClusters1 = function(contribs, K1)
	cluster::pam(contribs, K1, diss=FALSE)$id.med

#' @rdname clustering
#' @export
computeClusters2 = function(medoids, K2,
	getRefSeries, nb_ref_curves, nb_series_per_chunk, ncores_clust=1,verbose=FALSE,parll=TRUE)
{
	synchrones = computeSynchrones(medoids,
		getRefSeries, nb_ref_curves, nb_series_per_chunk, ncores_clust, verbose, parll)
	distances = computeWerDists(synchrones, ncores_clust, verbose, parll)
	#TODO: if PAM cannot take big.matrix in input, cast it before... (more than OK in RAM)
	medoids[ cluster::pam(distances, K2, diss=TRUE)$medoids , ]
}

#' computeSynchrones
#'
#' Compute the synchrones curves (sum of clusters elements) from a matrix of medoids,
#' using L2 distances.
#'
#' @param medoids big.matrix of medoids (curves of same length as initial series)
#' @param getRefSeries Function to retrieve initial series (e.g. in stage 2 after series
#'   have been replaced by stage-1 medoids)
#' @param nb_ref_curves How many reference series? (This number is known at this stage)
#' @inheritParams claws
#'
#' @return A big.matrix of size K1 x L where L = data_length
#'
#' @export
computeSynchrones = function(medoids, getRefSeries,
	nb_ref_curves, nb_series_per_chunk, ncores_clust=1,verbose=FALSE,parll=TRUE)
{


#TODO: si parll, getMedoids + serialization, pass only getMedoids to nodes
# --> BOF... chaque node chargera tous les medoids (efficacité) :/ ==> faut que ça tienne en RAM
#au pire :: C-ifier et charger medoids 1 by 1...

	#MIEUX :: medoids DOIT etre une big.matrix partagée !

	computeSynchronesChunk = function(indices)
	{
		if (verbose)
			cat(paste("--- Compute synchrones for ",length(indices)," lines\n", sep=""))
		ref_series = getRefSeries(indices)
		#get medoids indices for this chunk of series
		for (i in seq_len(nrow(ref_series)))
		{
			j = which.min( rowSums( sweep(medoids, 2, ref_series[i,], '-')^2 ) )
			if (parll)
				synchronicity::lock(m)
			synchrones[j,] = synchrones[j,] + ref_series[i,]
			counts[j,1] = counts[j,1] + 1
			if (parll)
				synchronicity::unlock(m)
		}
	}

	K = nrow(medoids)
	# Use bigmemory (shared==TRUE by default) + synchronicity to fill synchrones in //
	# TODO: if size > RAM (not our case), use file-backed big.matrix
	synchrones = bigmemory::big.matrix(nrow=K,ncol=ncol(medoids),type="double",init=0.)
	counts = bigmemory::big.matrix(nrow=K,ncol=1,type="double",init=0)
	# synchronicity is only for Linux & MacOS; on Windows: run sequentially
	parll = (requireNamespace("synchronicity",quietly=TRUE)
		&& parll && Sys.info()['sysname'] != "Windows")
	if (parll)
		m <- synchronicity::boost.mutex()

	if (parll)
	{
		cl = parallel::makeCluster(ncores_clust)
		parallel::clusterExport(cl,
			varlist=c("synchrones","counts","verbose","medoids","getRefSeries"),
			envir=environment())
	}

	indices_workers = .spreadIndices(seq_len(nb_ref_curves), nb_series_per_chunk)
	ignored <-
		if (parll)
			parallel::parLapply(indices_workers, computeSynchronesChunk)
		else
			lapply(indices_workers, computeSynchronesChunk)

	if (parll)
		parallel::stopCluster(cl)

	#TODO: can we avoid this loop? ( synchrones = sweep(synchrones, 1, counts, '/') )
	for (i in seq_len(K))
		synchrones[i,] = synchrones[i,] / counts[i,1]
	#NOTE: odds for some clusters to be empty? (when series already come from stage 2)
	#      ...maybe; but let's hope resulting K1' be still quite bigger than K2
	noNA_rows = sapply(seq_len(K), function(i) all(!is.nan(synchrones[i,])))
	if (all(noNA_rows))
		return (synchrones)
	# Else: some clusters are empty, need to slice synchrones
	synchrones[noNA_rows,]
}

#' computeWerDists
#'
#' Compute the WER distances between the synchrones curves (in rows), which are
#' returned (e.g.) by \code{computeSynchrones()}
#'
#' @param synchrones A big.matrix of synchrones, in rows. The series have same length
#'   as the series in the initial dataset
#' @inheritParams claws
#'
#' @return A big.matrix of size K1 x K1
#'
#' @export
computeWerDists = function(synchrones, ncores_clust=1,verbose=FALSE,parll=TRUE)
{


#TODO: re-organize to call computeWerDist(x,y) [C] (in //?) from two indices + big.matrix


	n <- nrow(synchrones)
	delta <- ncol(synchrones)
	#TODO: automatic tune of all these parameters ? (for other users)
	nvoice   <- 4
	# noctave = 2^13 = 8192 half hours ~ 180 days ; ~log2(ncol(synchrones))
	noctave = 13
	# 4 here represent 2^5 = 32 half-hours ~ 1 day
	#NOTE: default scalevector == 2^(0:(noctave * nvoice) / nvoice) * s0 (?)
	scalevector  <- 2^(4:(noctave * nvoice) / nvoice + 1)
	#condition: ( log2(s0*w0/(2*pi)) - 1 ) * nvoice + 1.5 >= 1
	s0=2
	w0=2*pi
	scaled=FALSE
	s0log = as.integer( (log2( s0*w0/(2*pi) ) - 1) * nvoice + 1.5 )
	totnoct = noctave + as.integer(s0log/nvoice) + 1

	computeCWT = function(i)
	{
		if (verbose)
			cat(paste("+++ Compute Rwave::cwt() on serie ",i,"\n", sep=""))
		ts <- scale(ts(synchrones[i,]), center=TRUE, scale=scaled)
		totts.cwt = Rwave::cwt(ts, totnoct, nvoice, w0, plot=FALSE)
		ts.cwt = totts.cwt[,s0log:(s0log+noctave*nvoice)]
		#Normalization
		sqs <- sqrt(2^(0:(noctave*nvoice)/nvoice)*s0)
		sqres <- sweep(ts.cwt,2,sqs,'*')
		sqres / max(Mod(sqres))
	}

	if (parll)
	{
		cl = parallel::makeCluster(ncores_clust)
		parallel::clusterExport(cl,
			varlist=c("synchrones","totnoct","nvoice","w0","s0log","noctave","s0","verbose"),
			envir=environment())
	}

	# list of CWT from synchrones
	# TODO: fit in RAM, OK? If not, 2 options: serialize, compute individual distances
	Xcwt4 <-
		if (parll)
			parallel::parLapply(cl, seq_len(n), computeCWT)
		else
			lapply(seq_len(n), computeCWT)

	if (parll)
		parallel::stopCluster(cl)

	Xwer_dist <- bigmemory::big.matrix(nrow=n, ncol=n, type="double")
	fcoefs = rep(1/3, 3) #moving average on 3 values (TODO: very slow! correct?!)
	if (verbose)
		cat("*** Compute WER distances from CWT\n")

	#TODO: computeDistances(i,j), et répartir les n(n-1)/2 couples d'indices
	#là c'est trop déséquilibré

	computeDistancesLineI = function(i)
	{
		if (verbose)
			cat(paste("   Line ",i,"\n", sep=""))
		for (j in (i+1):n)
		{
			#TODO: 'circular=TRUE' is wrong, should just take values on the sides; to rewrite in C
			num <- filter(Mod(Xcwt4[[i]] * Conj(Xcwt4[[j]])), fcoefs, circular=TRUE)
			WX <- filter(Mod(Xcwt4[[i]] * Conj(Xcwt4[[i]])), fcoefs, circular=TRUE)
			WY <- filter(Mod(Xcwt4[[j]] * Conj(Xcwt4[[j]])), fcoefs, circular=TRUE)
			wer2 <- sum(colSums(num)^2) / sum( sum(colSums(WX) * colSums(WY)) )
			if (parll)
				synchronicity::lock(m)
			Xwer_dist[i,j] <- sqrt(delta * ncol(Xcwt4[[1]]) * (1 - wer2))
			Xwer_dist[j,i] <- Xwer_dist[i,j]
			if (parll)
				synchronicity::unlock(m)
		}
		Xwer_dist[i,i] = 0.
	}

	parll = (requireNamespace("synchronicity",quietly=TRUE)
		&& parll && Sys.info()['sysname'] != "Windows")
	if (parll)
		m <- synchronicity::boost.mutex()

	ignored <-
		if (parll)
		{
			parallel::mclapply(seq_len(n-1), computeDistancesLineI,
				mc.cores=ncores_clust, mc.allow.recursive=FALSE)
		}
		else
			lapply(seq_len(n-1), computeDistancesLineI)
	Xwer_dist[n,n] = 0.
	Xwer_dist
}

# Helper function to divide indices into balanced sets
.spreadIndices = function(indices, nb_per_chunk)
{
	L = length(indices)
	nb_workers = floor( L / nb_per_chunk )
	if (nb_workers == 0)
	{
		# L < nb_series_per_chunk, simple case
		indices_workers = list(indices)
	}
	else
	{
		indices_workers = lapply( seq_len(nb_workers), function(i)
			indices[(nb_per_chunk*(i-1)+1):(nb_per_chunk*i)] )
		# Spread the remaining load among the workers
		rem = L %% nb_per_chunk
		while (rem > 0)
		{
			index = rem%%nb_workers + 1
			indices_workers[[index]] = c(indices_workers[[index]], indices[L-rem+1])
			rem = rem - 1
		}
	}
	indices_workers
}
Commit	Line	Data
	1	#' @name clustering
	2	#' @rdname clustering
	3	#' @aliases clusteringTask1 computeClusters1 computeClusters2
	4	#'
	5	#' @title Two-stage clustering, withing one task (see \code{claws()})
	6	#'
	7	#' @description \code{clusteringTask1()} runs one full stage-1 task, which consists in
	8	#' iterated stage 1 clustering (on nb_curves / ntasks energy contributions, computed
	9	#' through discrete wavelets coefficients). \code{computeClusters1()} and
	10	#' \code{computeClusters2()} correspond to the atomic clustering procedures respectively
	11	#' for stage 1 and 2. The former applies the clustering algorithm (PAM) on a
	12	#' contributions matrix, while the latter clusters a chunk of series inside one task
	13	#' (~max nb_series_per_chunk)
	14	#'
	15	#' @param indices Range of series indices to cluster in parallel (initial data)
	16	#' @param getContribs Function to retrieve contributions from initial series indices:
	17	#' \code{getContribs(indices)} outpus a contributions matrix
	18	#' @param contribs matrix of contributions (e.g. output of \code{curvesToContribs()})
	19	#' @inheritParams computeSynchrones
	20	#' @inheritParams claws
	21	#'
	22	#' @return For \code{clusteringTask1()} and \code{computeClusters1()}, the indices of the
	23	#' computed (K1) medoids. Indices are irrelevant for stage 2 clustering, thus
	24	#' \code{computeClusters2()} outputs a big.matrix of medoids
	25	#' (of size limited by nb_series_per_chunk)
	26	NULL
	27
	28	#' @rdname clustering
	29	#' @export
	30	clusteringTask1 = function(
	31	indices, getContribs, K1, nb_series_per_chunk, ncores_clust=1, verbose=FALSE, parll=TRUE)
	32	{
	33	if (verbose)
	34	cat(paste("*** Clustering task on ",length(indices)," lines\n", sep=""))
	35
	36	wrapComputeClusters1 = function(inds) {
	37	if (parll)
	38	require("epclust", quietly=TRUE)
	39	if (verbose)
	40	cat(paste(" computeClusters1() on ",length(inds)," lines\n", sep=""))
	41	inds[ computeClusters1(getContribs(inds), K1) ]
	42	}
	43
	44	if (parll)
	45	{
	46	cl = parallel::makeCluster(ncores_clust)
	47	parallel::clusterExport(cl, varlist=c("getContribs","K1","verbose"), envir=environment())
	48	}
	49	while (length(indices) > K1)
	50	{
	51	indices_workers = .spreadIndices(indices, nb_series_per_chunk)
	52	if (parll)
	53	indices = unlist( parallel::parLapply(cl, indices_workers, wrapComputeClusters1) )
	54	else
	55	indices = unlist( lapply(indices_workers, wrapComputeClusters1) )
	56	}
	57	if (parll)
	58	parallel::stopCluster(cl)
	59
	60	indices #medoids
	61	}
	62
	63	#' @rdname clustering
	64	#' @export
	65	computeClusters1 = function(contribs, K1)
	66	cluster::pam(contribs, K1, diss=FALSE)$id.med
	67
	68	#' @rdname clustering
	69	#' @export
	70	computeClusters2 = function(medoids, K2,
	71	getRefSeries, nb_ref_curves, nb_series_per_chunk, ncores_clust=1,verbose=FALSE,parll=TRUE)
	72	{
	73	synchrones = computeSynchrones(medoids,
	74	getRefSeries, nb_ref_curves, nb_series_per_chunk, ncores_clust, verbose, parll)
	75	distances = computeWerDists(synchrones, ncores_clust, verbose, parll)
	76	#TODO: if PAM cannot take big.matrix in input, cast it before... (more than OK in RAM)
	77	medoids[ cluster::pam(distances, K2, diss=TRUE)$medoids , ]
	78	}
	79
	80	#' computeSynchrones
	81	#'
	82	#' Compute the synchrones curves (sum of clusters elements) from a matrix of medoids,
	83	#' using L2 distances.
	84	#'
	85	#' @param medoids big.matrix of medoids (curves of same length as initial series)
	86	#' @param getRefSeries Function to retrieve initial series (e.g. in stage 2 after series
	87	#' have been replaced by stage-1 medoids)
	88	#' @param nb_ref_curves How many reference series? (This number is known at this stage)
	89	#' @inheritParams claws
	90	#'
	91	#' @return A big.matrix of size K1 x L where L = data_length
	92	#'
	93	#' @export
	94	computeSynchrones = function(medoids, getRefSeries,
	95	nb_ref_curves, nb_series_per_chunk, ncores_clust=1,verbose=FALSE,parll=TRUE)
	96	{
	97
	98
	99
	100	#TODO: si parll, getMedoids + serialization, pass only getMedoids to nodes
	101	# --> BOF... chaque node chargera tous les medoids (efficacité) :/ ==> faut que ça tienne en RAM
	102	#au pire :: C-ifier et charger medoids 1 by 1...
	103
	104	#MIEUX :: medoids DOIT etre une big.matrix partagée !
	105
	106	computeSynchronesChunk = function(indices)
	107	{
	108	if (verbose)
	109	cat(paste("--- Compute synchrones for ",length(indices)," lines\n", sep=""))
	110	ref_series = getRefSeries(indices)
	111	#get medoids indices for this chunk of series
	112	for (i in seq_len(nrow(ref_series)))
	113	{
	114	j = which.min( rowSums( sweep(medoids, 2, ref_series[i,], '-')^2 ) )
	115	if (parll)
	116	synchronicity::lock(m)
	117	synchrones[j,] = synchrones[j,] + ref_series[i,]
	118	counts[j,1] = counts[j,1] + 1
	119	if (parll)
	120	synchronicity::unlock(m)
	121	}
	122	}
	123
	124	K = nrow(medoids)
	125	# Use bigmemory (shared==TRUE by default) + synchronicity to fill synchrones in //
	126	# TODO: if size > RAM (not our case), use file-backed big.matrix
	127	synchrones = bigmemory::big.matrix(nrow=K,ncol=ncol(medoids),type="double",init=0.)
	128	counts = bigmemory::big.matrix(nrow=K,ncol=1,type="double",init=0)
	129	# synchronicity is only for Linux & MacOS; on Windows: run sequentially
	130	parll = (requireNamespace("synchronicity",quietly=TRUE)
	131	&& parll && Sys.info()['sysname'] != "Windows")
	132	if (parll)
	133	m <- synchronicity::boost.mutex()
	134
	135	if (parll)
	136	{
	137	cl = parallel::makeCluster(ncores_clust)
	138	parallel::clusterExport(cl,
	139	varlist=c("synchrones","counts","verbose","medoids","getRefSeries"),
	140	envir=environment())
	141	}
	142
	143	indices_workers = .spreadIndices(seq_len(nb_ref_curves), nb_series_per_chunk)
	144	ignored <-
	145	if (parll)
	146	parallel::parLapply(indices_workers, computeSynchronesChunk)
	147	else
	148	lapply(indices_workers, computeSynchronesChunk)
	149
	150	if (parll)
	151	parallel::stopCluster(cl)
	152
	153	#TODO: can we avoid this loop? ( synchrones = sweep(synchrones, 1, counts, '/') )
	154	for (i in seq_len(K))
	155	synchrones[i,] = synchrones[i,] / counts[i,1]
	156	#NOTE: odds for some clusters to be empty? (when series already come from stage 2)
	157	# ...maybe; but let's hope resulting K1' be still quite bigger than K2
	158	noNA_rows = sapply(seq_len(K), function(i) all(!is.nan(synchrones[i,])))
	159	if (all(noNA_rows))
	160	return (synchrones)
	161	# Else: some clusters are empty, need to slice synchrones
	162	synchrones[noNA_rows,]
	163	}
	164
	165	#' computeWerDists
	166	#'
	167	#' Compute the WER distances between the synchrones curves (in rows), which are
	168	#' returned (e.g.) by \code{computeSynchrones()}
	169	#'
	170	#' @param synchrones A big.matrix of synchrones, in rows. The series have same length
	171	#' as the series in the initial dataset
	172	#' @inheritParams claws
	173	#'
	174	#' @return A big.matrix of size K1 x K1
	175	#'
	176	#' @export
	177	computeWerDists = function(synchrones, ncores_clust=1,verbose=FALSE,parll=TRUE)
	178	{
	179
	180
	181
	182	#TODO: re-organize to call computeWerDist(x,y) [C] (in //?) from two indices + big.matrix
	183
	184
	185	n <- nrow(synchrones)
	186	delta <- ncol(synchrones)
	187	#TODO: automatic tune of all these parameters ? (for other users)
	188	nvoice <- 4
	189	# noctave = 2^13 = 8192 half hours ~ 180 days ; ~log2(ncol(synchrones))
	190	noctave = 13
	191	# 4 here represent 2^5 = 32 half-hours ~ 1 day
	192	#NOTE: default scalevector == 2^(0:(noctave * nvoice) / nvoice) * s0 (?)
	193	scalevector <- 2^(4:(noctave * nvoice) / nvoice + 1)
	194	#condition: ( log2(s0w0/(2pi)) - 1 ) * nvoice + 1.5 >= 1
	195	s0=2
	196	w0=2*pi
	197	scaled=FALSE
	198	s0log = as.integer( (log2( s0w0/(2pi) ) - 1) * nvoice + 1.5 )
	199	totnoct = noctave + as.integer(s0log/nvoice) + 1
	200
	201	computeCWT = function(i)
	202	{
	203	if (verbose)
	204	cat(paste("+++ Compute Rwave::cwt() on serie ",i,"\n", sep=""))
	205	ts <- scale(ts(synchrones[i,]), center=TRUE, scale=scaled)
	206	totts.cwt = Rwave::cwt(ts, totnoct, nvoice, w0, plot=FALSE)
	207	ts.cwt = totts.cwt[,s0log:(s0log+noctave*nvoice)]
	208	#Normalization
	209	sqs <- sqrt(2^(0:(noctavenvoice)/nvoice)s0)
	210	sqres <- sweep(ts.cwt,2,sqs,'*')
	211	sqres / max(Mod(sqres))
	212	}
	213
	214	if (parll)
	215	{
	216	cl = parallel::makeCluster(ncores_clust)
	217	parallel::clusterExport(cl,
	218	varlist=c("synchrones","totnoct","nvoice","w0","s0log","noctave","s0","verbose"),
	219	envir=environment())
	220	}
	221
	222	# list of CWT from synchrones
	223	# TODO: fit in RAM, OK? If not, 2 options: serialize, compute individual distances
	224	Xcwt4 <-
	225	if (parll)
	226	parallel::parLapply(cl, seq_len(n), computeCWT)
	227	else
	228	lapply(seq_len(n), computeCWT)
	229
	230	if (parll)
	231	parallel::stopCluster(cl)
	232
	233	Xwer_dist <- bigmemory::big.matrix(nrow=n, ncol=n, type="double")
	234	fcoefs = rep(1/3, 3) #moving average on 3 values (TODO: very slow! correct?!)
	235	if (verbose)
	236	cat("*** Compute WER distances from CWT\n")
	237
	238	#TODO: computeDistances(i,j), et répartir les n(n-1)/2 couples d'indices
	239	#là c'est trop déséquilibré
	240
	241	computeDistancesLineI = function(i)
	242	{
	243	if (verbose)
	244	cat(paste(" Line ",i,"\n", sep=""))
	245	for (j in (i+1):n)
	246	{
	247	#TODO: 'circular=TRUE' is wrong, should just take values on the sides; to rewrite in C
	248	num <- filter(Mod(Xcwt4[[i]] * Conj(Xcwt4[[j]])), fcoefs, circular=TRUE)
	249	WX <- filter(Mod(Xcwt4[[i]] * Conj(Xcwt4[[i]])), fcoefs, circular=TRUE)
	250	WY <- filter(Mod(Xcwt4[[j]] * Conj(Xcwt4[[j]])), fcoefs, circular=TRUE)
	251	wer2 <- sum(colSums(num)^2) / sum( sum(colSums(WX) * colSums(WY)) )
	252	if (parll)
	253	synchronicity::lock(m)
	254	Xwer_dist[i,j] <- sqrt(delta * ncol(Xcwt4[[1]]) * (1 - wer2))
	255	Xwer_dist[j,i] <- Xwer_dist[i,j]
	256	if (parll)
	257	synchronicity::unlock(m)
	258	}
	259	Xwer_dist[i,i] = 0.
	260	}
	261
	262	parll = (requireNamespace("synchronicity",quietly=TRUE)
	263	&& parll && Sys.info()['sysname'] != "Windows")
	264	if (parll)
	265	m <- synchronicity::boost.mutex()
	266
	267	ignored <-
	268	if (parll)
	269	{
	270	parallel::mclapply(seq_len(n-1), computeDistancesLineI,
	271	mc.cores=ncores_clust, mc.allow.recursive=FALSE)
	272	}
	273	else
	274	lapply(seq_len(n-1), computeDistancesLineI)
	275	Xwer_dist[n,n] = 0.
	276	Xwer_dist
	277	}
	278
	279	# Helper function to divide indices into balanced sets
	280	.spreadIndices = function(indices, nb_per_chunk)
	281	{
	282	L = length(indices)
	283	nb_workers = floor( L / nb_per_chunk )
	284	if (nb_workers == 0)
	285	{
	286	# L < nb_series_per_chunk, simple case
	287	indices_workers = list(indices)
	288	}
	289	else
	290	{
	291	indices_workers = lapply( seq_len(nb_workers), function(i)
	292	indices[(nb_per_chunk(i-1)+1):(nb_per_chunki)] )
	293	# Spread the remaining load among the workers
	294	rem = L %% nb_per_chunk
	295	while (rem > 0)
	296	{
	297	index = rem%%nb_workers + 1
	298	indices_workers[[index]] = c(indices_workers[[index]], indices[L-rem+1])
	299	rem = rem - 1
	300	}
	301	}
	302	indices_workers
	303	}