[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 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)
	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 Matrix of medoids (curves of same legnth 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
#'
#' @export
computeSynchrones = function(medoids, getRefSeries,
	nb_ref_curves, nb_series_per_chunk, ncores_clust=1,verbose=FALSE,parll=TRUE)
{
	computeSynchronesChunk = function(indices)
	{
		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 //
	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)
	# Fork (// run) only on Linux & MacOS; on Windows: run sequentially
	parll = (requireNamespace("synchronicity",quietly=TRUE)
		&& parll && Sys.info()['sysname'] != "Windows")
	if (parll)
		m <- synchronicity::boost.mutex()

	indices_workers = .spreadIndices(seq_len(nb_ref_curves), nb_series_per_chunk)
	for (inds in indices_workers)
	{
		if (verbose)
		{
			cat(paste("--- Compute synchrones for indices range ",
				min(inds)," -> ",max(inds),"\n", sep=""))
		}
		if (parll)
			ignored <- parallel::mcparallel(computeSynchronesChunk(inds))
		else
			computeSynchronesChunk(inds)
	}
	if (parll)
		parallel::mccollect()

	mat_syncs = matrix(nrow=K, ncol=ncol(medoids))
	vec_count = rep(NA, K)
	#TODO: can we avoid this loop?
	for (i in seq_len(K))
	{
		mat_syncs[i,] = synchrones[i,]
		vec_count[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
	mat_syncs = sweep(mat_syncs, 1, vec_count, '/')
	mat_syncs[ sapply(seq_len(K), function(i) all(!is.nan(mat_syncs[i,]))) , ]
}

#' computeWerDists
#'
#' Compute the WER distances between the synchrones curves (in rows), which are
#' returned (e.g.) by \code{computeSynchrones()}
#'
#' @param synchrones A matrix of synchrones, in rows. The series have same length as the
#'   series in the initial dataset
#' @inheritParams claws
#'
#' @export
computeWerDists = function(synchrones, ncores_clust=1,verbose=FALSE,parll=TRUE)
{
	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) * 2
	#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=0)
		ts.cwt = totts.cwt[,s0log:(s0log+noctave*nvoice)]
		#Normalization
		sqs <- sqrt(2^(0:(noctave*nvoice)/nvoice)*s0)
		sqres <- sweep(ts.cwt,MARGIN=2,sqs,'*')
		sqres / max(Mod(sqres))
	}

	if (parll)
	{
		cl = parallel::makeCluster(ncores_clust)
		parallel::clusterExport(cl, varlist=c("getContribs","K1","verbose"), envir=environment())
	}

	# (normalized) observations node with CWT
	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")

	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()

	for (i in 1:(n-1))
	{
		if (parll)
			ignored <- parallel::mcparallel(computeDistancesLineI(i))
		else
			computeDistancesLineI(i)
	}
	Xwer_dist[n,n] = 0.

	if (parll)
		parallel::mccollect()

	mat_dists = matrix(nrow=n, ncol=n)
	#TODO: avoid this loop?
	for (i in 1:n)
		mat_dists[i,] = Xwer_dist[i,]
	mat_dists
}

# 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
4bcfdbee BA	1	#' @name clustering
4bcfdbee BA	2	#' @rdname clustering
492cd9e7	3	#' @aliases clusteringTask1 computeClusters1 computeClusters2
4bcfdbee	4	#'
492cd9e7	5	#' @title Two-stage clustering, withing one task (see \code{claws()})
4bcfdbee	6	#'
492cd9e7 BA	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)
4bcfdbee BA	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	#'
492cd9e7	22	#' @return For \code{clusteringTask1()} and \code{computeClusters1()}, the indices of the
4bcfdbee BA	23	#' computed (K1) medoids. Indices are irrelevant for stage 2 clustering, thus
	24	#' \code{computeClusters2()} outputs a matrix of medoids
	25	#' (of size limited by nb_series_per_chunk)
	26	NULL
	27
	28	#' @rdname clustering
	29	#' @export
492cd9e7 BA	30	clusteringTask1 = function(
492cd9e7 BA	31	indices, getContribs, K1, nb_series_per_chunk, ncores_clust=1, verbose=FALSE, parll=TRUE)
5c652979	32	{
492cd9e7 BA	33	if (verbose)
492cd9e7 BA	34	cat(paste("*** Clustering task on ",length(indices)," lines\n", sep=""))
4bcfdbee	35
492cd9e7 BA	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	}
4bcfdbee	43
492cd9e7	44	if (parll)
7b13d0c2	45	{
492cd9e7 BA	46	cl = parallel::makeCluster(ncores_clust)
492cd9e7 BA	47	parallel::clusterExport(cl, varlist=c("getContribs","K1","verbose"), envir=environment())
7b13d0c2	48	}
492cd9e7 BA	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
56857861	60	indices #medoids
5c652979 BA	61	}
5c652979 BA	62
4bcfdbee BA	63	#' @rdname clustering
	64	#' @export
	65	computeClusters1 = function(contribs, K1)
	66	cluster::pam(contribs, K1, diss=FALSE)$id.med
0e2dce80	67
4bcfdbee BA	68	#' @rdname clustering
4bcfdbee BA	69	#' @export
492cd9e7 BA	70	computeClusters2 = function(medoids, K2,
492cd9e7 BA	71	getRefSeries, nb_ref_curves, nb_series_per_chunk, ncores_clust=1,verbose=FALSE,parll=TRUE)
5c652979	72	{
492cd9e7 BA	73	synchrones = computeSynchrones(medoids,
	74	getRefSeries, nb_ref_curves, nb_series_per_chunk, ncores_clust, verbose, parll)
	75	distances = computeWerDists(synchrones, ncores_clust, verbose, parll)
	76	medoids[ cluster::pam(distances, K2, diss=TRUE)$medoids , ]
5c652979 BA	77	}
5c652979 BA	78
4bcfdbee BA	79	#' computeSynchrones
	80	#'
	81	#' Compute the synchrones curves (sum of clusters elements) from a matrix of medoids,
	82	#' using L2 distances.
	83	#'
	84	#' @param medoids Matrix of medoids (curves of same legnth as initial series)
	85	#' @param getRefSeries Function to retrieve initial series (e.g. in stage 2 after series
	86	#' have been replaced by stage-1 medoids)
492cd9e7	87	#' @param nb_ref_curves How many reference series? (This number is known at this stage)
4bcfdbee BA	88	#' @inheritParams claws
	89	#'
	90	#' @export
492cd9e7 BA	91	computeSynchrones = function(medoids, getRefSeries,
492cd9e7 BA	92	nb_ref_curves, nb_series_per_chunk, ncores_clust=1,verbose=FALSE,parll=TRUE)
e205f218	93	{
492cd9e7	94	computeSynchronesChunk = function(indices)
3eef8d3d	95	{
492cd9e7	96	ref_series = getRefSeries(indices)
3eef8d3d	97	#get medoids indices for this chunk of series
56857861 BA	98	for (i in seq_len(nrow(ref_series)))
56857861 BA	99	{
8702eb86	100	j = which.min( rowSums( sweep(medoids, 2, ref_series[i,], '-')^2 ) )
492cd9e7 BA	101	if (parll)
492cd9e7 BA	102	synchronicity::lock(m)
8702eb86	103	synchrones[j,] = synchrones[j,] + ref_series[i,]
492cd9e7 BA	104	counts[j,1] = counts[j,1] + 1
	105	if (parll)
	106	synchronicity::unlock(m)
	107	}
	108	}
	109
	110	K = nrow(medoids)
	111	# Use bigmemory (shared==TRUE by default) + synchronicity to fill synchrones in //
	112	synchrones = bigmemory::big.matrix(nrow=K,ncol=ncol(medoids),type="double",init=0.)
	113	counts = bigmemory::big.matrix(nrow=K,ncol=1,type="double",init=0)
	114	# Fork (// run) only on Linux & MacOS; on Windows: run sequentially
	115	parll = (requireNamespace("synchronicity",quietly=TRUE)
	116	&& parll && Sys.info()['sysname'] != "Windows")
	117	if (parll)
	118	m <- synchronicity::boost.mutex()
	119
	120	indices_workers = .spreadIndices(seq_len(nb_ref_curves), nb_series_per_chunk)
	121	for (inds in indices_workers)
	122	{
	123	if (verbose)
	124	{
	125	cat(paste("--- Compute synchrones for indices range ",
	126	min(inds)," -> ",max(inds),"\n", sep=""))
56857861	127	}
492cd9e7 BA	128	if (parll)
	129	ignored <- parallel::mcparallel(computeSynchronesChunk(inds))
	130	else
	131	computeSynchronesChunk(inds)
	132	}
	133	if (parll)
	134	parallel::mccollect()
	135
	136	mat_syncs = matrix(nrow=K, ncol=ncol(medoids))
	137	vec_count = rep(NA, K)
	138	#TODO: can we avoid this loop?
	139	for (i in seq_len(K))
	140	{
	141	mat_syncs[i,] = synchrones[i,]
	142	vec_count[i] = counts[i,1]
3eef8d3d BA	143	}
3eef8d3d BA	144	#NOTE: odds for some clusters to be empty? (when series already come from stage 2)
8702eb86	145	# ...maybe; but let's hope resulting K1' be still quite bigger than K2
492cd9e7 BA	146	mat_syncs = sweep(mat_syncs, 1, vec_count, '/')
492cd9e7 BA	147	mat_syncs[ sapply(seq_len(K), function(i) all(!is.nan(mat_syncs[i,]))) , ]
e205f218	148	}
1c6f223e	149
4bcfdbee BA	150	#' computeWerDists
	151	#'
	152	#' Compute the WER distances between the synchrones curves (in rows), which are
	153	#' returned (e.g.) by \code{computeSynchrones()}
	154	#'
	155	#' @param synchrones A matrix of synchrones, in rows. The series have same length as the
492cd9e7 BA	156	#' series in the initial dataset
492cd9e7 BA	157	#' @inheritParams claws
4bcfdbee BA	158	#'
4bcfdbee BA	159	#' @export
492cd9e7	160	computeWerDists = function(synchrones, ncores_clust=1,verbose=FALSE,parll=TRUE)
d03c0621	161	{
4bcfdbee BA	162	n <- nrow(synchrones)
4bcfdbee BA	163	delta <- ncol(synchrones)
db6fc17d	164	#TODO: automatic tune of all these parameters ? (for other users)
d03c0621	165	nvoice <- 4
4bcfdbee	166	# noctave = 2^13 = 8192 half hours ~ 180 days ; ~log2(ncol(synchrones))
d7d55bc1 BA	167	noctave = 13
d7d55bc1 BA	168	# 4 here represent 2^5 = 32 half-hours ~ 1 day
db6fc17d BA	169	#NOTE: default scalevector == 2^(0:(noctave * nvoice) / nvoice) * s0 (?)
	170	scalevector <- 2^(4:(noctave * nvoice) / nvoice) * 2
	171	#condition: ( log2(s0w0/(2pi)) - 1 ) * nvoice + 1.5 >= 1
	172	s0=2
	173	w0=2*pi
	174	scaled=FALSE
	175	s0log = as.integer( (log2( s0w0/(2pi) ) - 1) * nvoice + 1.5 )
	176	totnoct = noctave + as.integer(s0log/nvoice) + 1
	177
492cd9e7 BA	178	computeCWT = function(i)
	179	{
	180	if (verbose)
	181	cat(paste("+++ Compute Rwave::cwt() on serie ",i,"\n", sep=""))
4bcfdbee	182	ts <- scale(ts(synchrones[i,]), center=TRUE, scale=scaled)
db6fc17d BA	183	totts.cwt = Rwave::cwt(ts,totnoct,nvoice,w0,plot=0)
	184	ts.cwt = totts.cwt[,s0log:(s0log+noctave*nvoice)]
	185	#Normalization
	186	sqs <- sqrt(2^(0:(noctavenvoice)/nvoice)s0)
	187	sqres <- sweep(ts.cwt,MARGIN=2,sqs,'*')
	188	sqres / max(Mod(sqres))
492cd9e7	189	}
3ccd1e39	190
492cd9e7 BA	191	if (parll)
	192	{
	193	cl = parallel::makeCluster(ncores_clust)
	194	parallel::clusterExport(cl, varlist=c("getContribs","K1","verbose"), envir=environment())
	195	}
	196
	197	# (normalized) observations node with CWT
	198	Xcwt4 <-
	199	if (parll)
	200	parallel::parLapply(cl, seq_len(n), computeCWT)
	201	else
	202	lapply(seq_len(n), computeCWT)
	203
	204	if (parll)
	205	parallel::stopCluster(cl)
	206
	207	Xwer_dist <- bigmemory::big.matrix(nrow=n, ncol=n, type="double")
db6fc17d	208	fcoefs = rep(1/3, 3) #moving average on 3 values (TODO: very slow! correct?!)
492cd9e7 BA	209	if (verbose)
	210	cat("*** Compute WER distances from CWT\n")
	211
	212	computeDistancesLineI = function(i)
1c6f223e	213	{
492cd9e7 BA	214	if (verbose)
492cd9e7 BA	215	cat(paste(" Line ",i,"\n", sep=""))
db6fc17d	216	for (j in (i+1):n)
d03c0621	217	{
492cd9e7	218	#TODO: 'circular=TRUE' is wrong, should just take values on the sides; to rewrite in C
db6fc17d BA	219	num <- filter(Mod(Xcwt4[[i]] * Conj(Xcwt4[[j]])), fcoefs, circular=TRUE)
	220	WX <- filter(Mod(Xcwt4[[i]] * Conj(Xcwt4[[i]])), fcoefs, circular=TRUE)
	221	WY <- filter(Mod(Xcwt4[[j]] * Conj(Xcwt4[[j]])), fcoefs, circular=TRUE)
	222	wer2 <- sum(colSums(num)^2) / sum( sum(colSums(WX) * colSums(WY)) )
492cd9e7 BA	223	if (parll)
492cd9e7 BA	224	synchronicity::lock(m)
db6fc17d BA	225	Xwer_dist[i,j] <- sqrt(delta * ncol(Xcwt4[[1]]) * (1 - wer2))
db6fc17d BA	226	Xwer_dist[j,i] <- Xwer_dist[i,j]
492cd9e7 BA	227	if (parll)
	228	synchronicity::unlock(m)
	229	}
	230	Xwer_dist[i,i] = 0.
	231	}
	232
	233	parll = (requireNamespace("synchronicity",quietly=TRUE)
	234	&& parll && Sys.info()['sysname'] != "Windows")
	235	if (parll)
	236	m <- synchronicity::boost.mutex()
	237
	238	for (i in 1:(n-1))
	239	{
	240	if (parll)
	241	ignored <- parallel::mcparallel(computeDistancesLineI(i))
	242	else
	243	computeDistancesLineI(i)
	244	}
	245	Xwer_dist[n,n] = 0.
	246
	247	if (parll)
	248	parallel::mccollect()
	249
	250	mat_dists = matrix(nrow=n, ncol=n)
	251	#TODO: avoid this loop?
	252	for (i in 1:n)
	253	mat_dists[i,] = Xwer_dist[i,]
	254	mat_dists
	255	}
	256
	257	# Helper function to divide indices into balanced sets
	258	.spreadIndices = function(indices, nb_per_chunk)
	259	{
	260	L = length(indices)
	261	nb_workers = floor( L / nb_per_chunk )
	262	if (nb_workers == 0)
	263	{
	264	# L < nb_series_per_chunk, simple case
	265	indices_workers = list(indices)
	266	}
	267	else
	268	{
	269	indices_workers = lapply( seq_len(nb_workers), function(i)
	270	indices[(nb_per_chunk(i-1)+1):(nb_per_chunki)] )
	271	# Spread the remaining load among the workers
	272	rem = L %% nb_per_chunk
	273	while (rem > 0)
	274	{
	275	index = rem%%nb_workers + 1
	276	indices_workers[[index]] = c(indices_workers[[index]], indices[L-rem+1])
	277	rem = rem - 1
d03c0621	278	}
1c6f223e	279	}
492cd9e7	280	indices_workers
1c6f223e	281	}