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

#' @name clustering
#' @rdname clustering
#' @aliases clusteringTask1 clusteringTask2 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{clusteringTask2()} runs a full stage-2 task, which consists in synchrones
#'   and then WER distances computations, before applying the clustering algorithm.
#'   \code{computeClusters1()} and \code{computeClusters2()} correspond to the atomic
#'   clustering procedures respectively for stage 1 and 2. The former applies the
#'   first clustering algorithm on a contributions matrix, while the latter clusters
#'   a set of series inside one task (~nb_items_clust1)
#'
#' @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
#' @inheritParams computeSynchrones
#' @inheritParams claws
#'
#' @return For \code{clusteringTask1()}, the indices of the computed (K1) medoids.
#'   Indices are irrelevant for stage 2 clustering, thus \code{clusteringTask2()}
#'   outputs a big.matrix of medoids (of size LxK2, K2 = final number of clusters)
NULL

#' @rdname clustering
#' @export
clusteringTask1 = function(indices, getContribs, K1, algoClust1, nb_items_clust1,
	ncores_clust=1, verbose=FALSE, parll=TRUE)
{
	if (parll)
	{
		cl = parallel::makeCluster(ncores_clust, outfile = "")
		parallel::clusterExport(cl, c("getContribs","K1","verbose"), envir=environment())
	}
	# Iterate clustering algorithm 1 until K1 medoids are found
	while (length(indices) > K1)
	{
		# Balance tasks by splitting the indices set - as evenly as possible
		indices_workers = .spreadIndices(indices, nb_items_clust1)
		if (verbose)
			cat(paste("*** [iterated] Clustering task 1 on ",length(indices)," series\n", sep=""))
		indices <-
			if (parll)
			{
				unlist( parallel::parLapply(cl, indices_workers, function(inds) {
					require("epclust", quietly=TRUE)
					inds[ algoClust1(getContribs(inds), K1) ]
				}) )
			}
			else
			{
				unlist( lapply(indices_workers, function(inds)
					inds[ algoClust1(getContribs(inds), K1) ]
				) )
			}
	}
	if (parll)
		parallel::stopCluster(cl)

	indices #medoids
}

#' @rdname clustering
#' @export
clusteringTask2 = function(medoids, K2, algoClust2, getRefSeries, nb_ref_curves,
	nb_series_per_chunk, nbytes,endian,ncores_clust=1,verbose=FALSE,parll=TRUE)
{
	if (verbose)
		cat(paste("*** Clustering task 2 on ",ncol(medoids)," synchrones\n", sep=""))

	if (ncol(medoids) <= K2)
		return (medoids)

	# A) Obtain synchrones, that is to say the cumulated power consumptions
	#    for each of the K1 initial groups
	synchrones = computeSynchrones(medoids, getRefSeries, nb_ref_curves,
		nb_series_per_chunk, ncores_clust, verbose, parll)

	# B) Compute the WER distances (Wavelets Extended coefficient of deteRmination)
	distances = computeWerDists(synchrones, nbytes, endian, ncores_clust, verbose, parll)

	# C) Apply clustering algorithm 2 on the WER distances matrix
	if (verbose)
		cat(paste("   algoClust2() on ",nrow(distances)," items\n", sep=""))
	medoids[ ,algoClust2(distances,K2) ]
}

#' computeSynchrones
#'
#' Compute the synchrones curves (sum of clusters elements) from a matrix of medoids,
#' using euclidian distance.
#'
#' @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 L x K1 where L = length of a serie
#'
#' @export
computeSynchrones = function(medoids, getRefSeries, nb_ref_curves,
	nb_series_per_chunk, ncores_clust=1,verbose=FALSE,parll=TRUE)
{
	# Synchrones computation is embarassingly parallel: compute it by chunks of series
	computeSynchronesChunk = function(indices)
	{
		if (parll)
		{
			require("bigmemory", quietly=TRUE)
			requireNamespace("synchronicity", quietly=TRUE)
			require("epclust", quietly=TRUE)
			# The big.matrix objects need to be attached to be usable on the workers
			synchrones <- bigmemory::attach.big.matrix(synchrones_desc)
			medoids <- bigmemory::attach.big.matrix(medoids_desc)
			m <- synchronicity::attach.mutex(m_desc)
		}

		# Obtain a chunk of reference series
		ref_series = getRefSeries(indices)
		nb_series = ncol(ref_series)

		# Get medoids indices for this chunk of series
		mi = computeMedoidsIndices(medoids@address, ref_series)

		# Update synchrones using mi above
		for (i in seq_len(nb_series))
		{
			if (parll)
				synchronicity::lock(m) #locking required because several writes at the same time
			synchrones[, mi[i] ] = synchrones[, mi[i] ] + ref_series[,i]
			if (parll)
				synchronicity::unlock(m)
		}
	}

	K = ncol(medoids) ; L = nrow(medoids)
	# Use bigmemory (shared==TRUE by default) + synchronicity to fill synchrones in //
	synchrones = bigmemory::big.matrix(nrow=L, ncol=K, type="double", init=0.)
	# NOTE: 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() #for lock/unlock, see computeSynchronesChunk
		# mutex and big.matrix objects cannot be passed directly:
		# they will be accessed from their description
		m_desc <- synchronicity::describe(m)
		synchrones_desc = bigmemory::describe(synchrones)
		medoids_desc = bigmemory::describe(medoids)
		cl = parallel::makeCluster(ncores_clust)
		parallel::clusterExport(cl, envir=environment(),
			varlist=c("synchrones_desc","m_desc","medoids_desc","getRefSeries"))
	}

	if (verbose)
		cat(paste("--- Compute ",K," synchrones with ",nb_ref_curves," series\n", sep=""))

	# Balance tasks by splitting the indices set - maybe not so evenly, but
	# max==TRUE in next call ensures that no set has more than nb_series_per_chunk items.
	indices_workers = .spreadIndices(seq_len(nb_ref_curves), nb_series_per_chunk, max=TRUE)
	ignored <-
		if (parll)
			parallel::parLapply(cl, indices_workers, computeSynchronesChunk)
		else
			lapply(indices_workers, computeSynchronesChunk)

	if (parll)
		parallel::stopCluster(cl)

	return (synchrones)
}

#' 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 matrix of size K1 x K1
#'
#' @export
computeWerDists = function(synchrones, nbytes,endian,ncores_clust=1,verbose=FALSE,parll=TRUE)
{
	n <- ncol(synchrones)
	L <- nrow(synchrones)
	#TODO: automatic tune of all these parameters ? (for other users)
	# 4 here represent 2^5 = 32 half-hours ~ 1 day
	nvoice   <- 4
	# noctave = 2^13 = 8192 half hours ~ 180 days ; ~log2(ncol(synchrones))
	noctave = 13

	Xwer_dist <- bigmemory::big.matrix(nrow=n, ncol=n, type="double")

	cwt_file = ".epclust_bin/cwt"
	#TODO: args, nb_per_chunk, nbytes, endian

	# Generate n(n-1)/2 pairs for WER distances computations
	pairs = list()
	V = seq_len(n)
	for (i in 1:n)
	{
		V = V[-1]
		pairs = c(pairs, lapply(V, function(v) c(i,v)))
	}

	computeSaveCWT = function(index)
	{
		ts <- scale(ts(synchrones[,index]), center=TRUE, scale=FALSE)
		totts.cwt = Rwave::cwt(ts, totnoct, nvoice, w0=2*pi, twoD=TRUE, 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,'*')
		res <- sqres / max(Mod(sqres))
		#TODO: serializer les CWT, les récupérer via getDataInFile ;
		#--> OK, faut juste stocker comme séries simples de taille L*n' (53*17519)
		binarize(c(as.double(Re(res)),as.double(Im(res))), cwt_file, ncol(res), ",", nbytes, endian)
	}

	if (parll)
	{
		cl = parallel::makeCluster(ncores_clust)
		synchrones_desc <- bigmemory::describe(synchrones)
		Xwer_dist_desc <- bigmemory::describe(Xwer_dist)
		parallel::clusterExport(cl, envir=environment(),
			varlist=c("synchrones_desc","Xwer_dist_desc","totnoct","nvoice","w0","s0log",
				"noctave","s0","verbose","getCWT"))
	}
	
	if (verbose)
	{
		cat(paste("--- Compute WER dists\n", sep=""))
	#	precompute save all CWT........
	}
	#precompute and serialize all CWT
	ignored <-
		if (parll)
			parallel::parLapply(cl, 1:n, computeSaveCWT)
		else
			lapply(1:n, computeSaveCWT)

	getCWT = function(index)
	{
		#from cwt_file ...
		res <- getDataInFile(c(2*index-1,2*index), cwt_file, nbytes, endian)
	###############TODO:
	}

	# Distance between rows i and j
	computeDistancesIJ = function(pair)
	{
		if (parll)
		{
			require("bigmemory", quietly=TRUE)
			require("epclust", quietly=TRUE)
			synchrones <- bigmemory::attach.big.matrix(synchrones_desc)
			Xwer_dist <- bigmemory::attach.big.matrix(Xwer_dist_desc)
		}

		i = pair[1] ; j = pair[2]
		if (verbose && j==i+1)
			cat(paste("   Distances (",i,",",j,"), (",i,",",j+1,") ...\n", sep=""))
		cwt_i <- getCWT(i)
		cwt_j <- getCWT(j)

		num <- epclustFilter(Mod(cwt_i * Conj(cwt_j)))
		WX  <- epclustFilter(Mod(cwt_i * Conj(cwt_i)))
		WY <- epclustFilter(Mod(cwt_j * Conj(cwt_j)))
		wer2 <- sum(colSums(num)^2) / sum(colSums(WX) * colSums(WY))
		Xwer_dist[i,j] <- sqrt(L * ncol(cwt_i) * max(1 - wer2, 0.))
		Xwer_dist[j,i] <- Xwer_dist[i,j]
		Xwer_dist[i,i] = 0.
	}

	if (verbose)
	{
		cat(paste("--- Compute WER dists\n", sep=""))
	}
	ignored <-
		if (parll)
			parallel::parLapply(cl, pairs, computeDistancesIJ)
		else
			lapply(pairs, computeDistancesIJ)

	if (parll)
		parallel::stopCluster(cl)

	Xwer_dist[n,n] = 0.
	distances <- Xwer_dist[,]
	rm(Xwer_dist) ; gc()
	distances #~small matrix K1 x K1
}

# Helper function to divide indices into balanced sets
# If max == TRUE, sets sizes cannot exceed nb_per_set
.spreadIndices = function(indices, nb_per_set, max=FALSE)
{
	L = length(indices)
	nb_workers = floor( L / nb_per_set )
	rem = L %% nb_per_set
	if (nb_workers == 0 || (nb_workers==1 && rem==0))
	{
		# L <= nb_per_set, simple case
		indices_workers = list(indices)
	}
	else
	{
		indices_workers = lapply( seq_len(nb_workers), function(i)
			indices[(nb_per_set*(i-1)+1):(nb_per_set*i)] )

		if (max)
		{
			# Sets are not so well balanced, but size is supposed to be critical
			return ( c( indices_workers, (L-rem+1):L ) )
		}

		# Spread the remaining load among the workers
		rem = L %% nb_per_set
		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 clusteringTask2 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).
	10	#' \code{clusteringTask2()} runs a full stage-2 task, which consists in synchrones
	11	#' and then WER distances computations, before applying the clustering algorithm.
	12	#' \code{computeClusters1()} and \code{computeClusters2()} correspond to the atomic
	13	#' clustering procedures respectively for stage 1 and 2. The former applies the
	14	#' first clustering algorithm on a contributions matrix, while the latter clusters
	15	#' a set of series inside one task (~nb_items_clust1)
	16	#'
	17	#' @param indices Range of series indices to cluster in parallel (initial data)
	18	#' @param getContribs Function to retrieve contributions from initial series indices:
	19	#' \code{getContribs(indices)} outpus a contributions matrix
	20	#' @inheritParams computeSynchrones
	21	#' @inheritParams claws
	22	#'
	23	#' @return For \code{clusteringTask1()}, the indices of the computed (K1) medoids.
	24	#' Indices are irrelevant for stage 2 clustering, thus \code{clusteringTask2()}
	25	#' outputs a big.matrix of medoids (of size LxK2, K2 = final number of clusters)
	26	NULL
	27
	28	#' @rdname clustering
	29	#' @export
	30	clusteringTask1 = function(indices, getContribs, K1, algoClust1, nb_items_clust1,
	31	ncores_clust=1, verbose=FALSE, parll=TRUE)
	32	{
	33	if (parll)
	34	{
	35	cl = parallel::makeCluster(ncores_clust, outfile = "")
	36	parallel::clusterExport(cl, c("getContribs","K1","verbose"), envir=environment())
	37	}
	38	# Iterate clustering algorithm 1 until K1 medoids are found
	39	while (length(indices) > K1)
	40	{
	41	# Balance tasks by splitting the indices set - as evenly as possible
	42	indices_workers = .spreadIndices(indices, nb_items_clust1)
	43	if (verbose)
	44	cat(paste("*** [iterated] Clustering task 1 on ",length(indices)," series\n", sep=""))
	45	indices <-
	46	if (parll)
	47	{
	48	unlist( parallel::parLapply(cl, indices_workers, function(inds) {
	49	require("epclust", quietly=TRUE)
	50	inds[ algoClust1(getContribs(inds), K1) ]
	51	}) )
	52	}
	53	else
	54	{
	55	unlist( lapply(indices_workers, function(inds)
	56	inds[ algoClust1(getContribs(inds), K1) ]
	57	) )
	58	}
	59	}
	60	if (parll)
	61	parallel::stopCluster(cl)
	62
	63	indices #medoids
	64	}
	65
	66	#' @rdname clustering
	67	#' @export
	68	clusteringTask2 = function(medoids, K2, algoClust2, getRefSeries, nb_ref_curves,
	69	nb_series_per_chunk, nbytes,endian,ncores_clust=1,verbose=FALSE,parll=TRUE)
	70	{
	71	if (verbose)
	72	cat(paste("*** Clustering task 2 on ",ncol(medoids)," synchrones\n", sep=""))
	73
	74	if (ncol(medoids) <= K2)
	75	return (medoids)
	76
	77	# A) Obtain synchrones, that is to say the cumulated power consumptions
	78	# for each of the K1 initial groups
	79	synchrones = computeSynchrones(medoids, getRefSeries, nb_ref_curves,
	80	nb_series_per_chunk, ncores_clust, verbose, parll)
	81
	82	# B) Compute the WER distances (Wavelets Extended coefficient of deteRmination)
	83	distances = computeWerDists(synchrones, nbytes, endian, ncores_clust, verbose, parll)
	84
	85	# C) Apply clustering algorithm 2 on the WER distances matrix
	86	if (verbose)
	87	cat(paste(" algoClust2() on ",nrow(distances)," items\n", sep=""))
	88	medoids[ ,algoClust2(distances,K2) ]
	89	}
	90
	91	#' computeSynchrones
	92	#'
	93	#' Compute the synchrones curves (sum of clusters elements) from a matrix of medoids,
	94	#' using euclidian distance.
	95	#'
	96	#' @param medoids big.matrix of medoids (curves of same length as initial series)
	97	#' @param getRefSeries Function to retrieve initial series (e.g. in stage 2 after series
	98	#' have been replaced by stage-1 medoids)
	99	#' @param nb_ref_curves How many reference series? (This number is known at this stage)
	100	#' @inheritParams claws
	101	#'
	102	#' @return A big.matrix of size L x K1 where L = length of a serie
	103	#'
	104	#' @export
	105	computeSynchrones = function(medoids, getRefSeries, nb_ref_curves,
	106	nb_series_per_chunk, ncores_clust=1,verbose=FALSE,parll=TRUE)
	107	{
	108	# Synchrones computation is embarassingly parallel: compute it by chunks of series
	109	computeSynchronesChunk = function(indices)
	110	{
	111	if (parll)
	112	{
	113	require("bigmemory", quietly=TRUE)
	114	requireNamespace("synchronicity", quietly=TRUE)
	115	require("epclust", quietly=TRUE)
	116	# The big.matrix objects need to be attached to be usable on the workers
	117	synchrones <- bigmemory::attach.big.matrix(synchrones_desc)
	118	medoids <- bigmemory::attach.big.matrix(medoids_desc)
	119	m <- synchronicity::attach.mutex(m_desc)
	120	}
	121
	122	# Obtain a chunk of reference series
	123	ref_series = getRefSeries(indices)
	124	nb_series = ncol(ref_series)
	125
	126	# Get medoids indices for this chunk of series
	127	mi = computeMedoidsIndices(medoids@address, ref_series)
	128
	129	# Update synchrones using mi above
	130	for (i in seq_len(nb_series))
	131	{
	132	if (parll)
	133	synchronicity::lock(m) #locking required because several writes at the same time
	134	synchrones[, mi[i] ] = synchrones[, mi[i] ] + ref_series[,i]
	135	if (parll)
	136	synchronicity::unlock(m)
	137	}
	138	}
	139
	140	K = ncol(medoids) ; L = nrow(medoids)
	141	# Use bigmemory (shared==TRUE by default) + synchronicity to fill synchrones in //
	142	synchrones = bigmemory::big.matrix(nrow=L, ncol=K, type="double", init=0.)
	143	# NOTE: synchronicity is only for Linux & MacOS; on Windows: run sequentially
	144	parll = (requireNamespace("synchronicity",quietly=TRUE)
	145	&& parll && Sys.info()['sysname'] != "Windows")
	146	if (parll)
	147	{
	148	m <- synchronicity::boost.mutex() #for lock/unlock, see computeSynchronesChunk
	149	# mutex and big.matrix objects cannot be passed directly:
	150	# they will be accessed from their description
	151	m_desc <- synchronicity::describe(m)
	152	synchrones_desc = bigmemory::describe(synchrones)
	153	medoids_desc = bigmemory::describe(medoids)
	154	cl = parallel::makeCluster(ncores_clust)
	155	parallel::clusterExport(cl, envir=environment(),
	156	varlist=c("synchrones_desc","m_desc","medoids_desc","getRefSeries"))
	157	}
	158
	159	if (verbose)
	160	cat(paste("--- Compute ",K," synchrones with ",nb_ref_curves," series\n", sep=""))
	161
	162	# Balance tasks by splitting the indices set - maybe not so evenly, but
	163	# max==TRUE in next call ensures that no set has more than nb_series_per_chunk items.
	164	indices_workers = .spreadIndices(seq_len(nb_ref_curves), nb_series_per_chunk, max=TRUE)
	165	ignored <-
	166	if (parll)
	167	parallel::parLapply(cl, indices_workers, computeSynchronesChunk)
	168	else
	169	lapply(indices_workers, computeSynchronesChunk)
	170
	171	if (parll)
	172	parallel::stopCluster(cl)
	173
	174	return (synchrones)
	175	}
	176
	177	#' computeWerDists
	178	#'
	179	#' Compute the WER distances between the synchrones curves (in rows), which are
	180	#' returned (e.g.) by \code{computeSynchrones()}
	181	#'
	182	#' @param synchrones A big.matrix of synchrones, in rows. The series have same length
	183	#' as the series in the initial dataset
	184	#' @inheritParams claws
	185	#'
	186	#' @return A matrix of size K1 x K1
	187	#'
	188	#' @export
	189	computeWerDists = function(synchrones, nbytes,endian,ncores_clust=1,verbose=FALSE,parll=TRUE)
	190	{
	191	n <- ncol(synchrones)
	192	L <- nrow(synchrones)
	193	#TODO: automatic tune of all these parameters ? (for other users)
	194	# 4 here represent 2^5 = 32 half-hours ~ 1 day
	195	nvoice <- 4
	196	# noctave = 2^13 = 8192 half hours ~ 180 days ; ~log2(ncol(synchrones))
	197	noctave = 13
	198
	199	Xwer_dist <- bigmemory::big.matrix(nrow=n, ncol=n, type="double")
	200
	201	cwt_file = ".epclust_bin/cwt"
	202	#TODO: args, nb_per_chunk, nbytes, endian
	203
	204	# Generate n(n-1)/2 pairs for WER distances computations
	205	pairs = list()
	206	V = seq_len(n)
	207	for (i in 1:n)
	208	{
	209	V = V[-1]
	210	pairs = c(pairs, lapply(V, function(v) c(i,v)))
	211	}
	212
	213	computeSaveCWT = function(index)
	214	{
	215	ts <- scale(ts(synchrones[,index]), center=TRUE, scale=FALSE)
	216	totts.cwt = Rwave::cwt(ts, totnoct, nvoice, w0=2*pi, twoD=TRUE, plot=FALSE)
	217	ts.cwt = totts.cwt[,s0log:(s0log+noctave*nvoice)]
	218	#Normalization
	219	sqs <- sqrt(2^(0:(noctavenvoice)/nvoice)s0)
	220	sqres <- sweep(ts.cwt,2,sqs,'*')
	221	res <- sqres / max(Mod(sqres))
	222	#TODO: serializer les CWT, les récupérer via getDataInFile ;
	223	#--> OK, faut juste stocker comme séries simples de taille Ln' (5317519)
	224	binarize(c(as.double(Re(res)),as.double(Im(res))), cwt_file, ncol(res), ",", nbytes, endian)
	225	}
	226
	227	if (parll)
	228	{
	229	cl = parallel::makeCluster(ncores_clust)
	230	synchrones_desc <- bigmemory::describe(synchrones)
	231	Xwer_dist_desc <- bigmemory::describe(Xwer_dist)
	232	parallel::clusterExport(cl, envir=environment(),
	233	varlist=c("synchrones_desc","Xwer_dist_desc","totnoct","nvoice","w0","s0log",
	234	"noctave","s0","verbose","getCWT"))
	235	}
	236
	237	if (verbose)
	238	{
	239	cat(paste("--- Compute WER dists\n", sep=""))
	240	# precompute save all CWT........
	241	}
	242	#precompute and serialize all CWT
	243	ignored <-
	244	if (parll)
	245	parallel::parLapply(cl, 1:n, computeSaveCWT)
	246	else
	247	lapply(1:n, computeSaveCWT)
	248
	249	getCWT = function(index)
	250	{
	251	#from cwt_file ...
	252	res <- getDataInFile(c(2index-1,2index), cwt_file, nbytes, endian)
	253	###############TODO:
	254	}
	255
	256	# Distance between rows i and j
	257	computeDistancesIJ = function(pair)
	258	{
	259	if (parll)
	260	{
	261	require("bigmemory", quietly=TRUE)
	262	require("epclust", quietly=TRUE)
	263	synchrones <- bigmemory::attach.big.matrix(synchrones_desc)
	264	Xwer_dist <- bigmemory::attach.big.matrix(Xwer_dist_desc)
	265	}
	266
	267	i = pair[1] ; j = pair[2]
	268	if (verbose && j==i+1)
	269	cat(paste(" Distances (",i,",",j,"), (",i,",",j+1,") ...\n", sep=""))
	270	cwt_i <- getCWT(i)
	271	cwt_j <- getCWT(j)
	272
	273	num <- epclustFilter(Mod(cwt_i * Conj(cwt_j)))
	274	WX <- epclustFilter(Mod(cwt_i * Conj(cwt_i)))
	275	WY <- epclustFilter(Mod(cwt_j * Conj(cwt_j)))
	276	wer2 <- sum(colSums(num)^2) / sum(colSums(WX) * colSums(WY))
	277	Xwer_dist[i,j] <- sqrt(L * ncol(cwt_i) * max(1 - wer2, 0.))
	278	Xwer_dist[j,i] <- Xwer_dist[i,j]
	279	Xwer_dist[i,i] = 0.
	280	}
	281
	282	if (verbose)
	283	{
	284	cat(paste("--- Compute WER dists\n", sep=""))
	285	}
	286	ignored <-
	287	if (parll)
	288	parallel::parLapply(cl, pairs, computeDistancesIJ)
	289	else
	290	lapply(pairs, computeDistancesIJ)
	291
	292	if (parll)
	293	parallel::stopCluster(cl)
	294
	295	Xwer_dist[n,n] = 0.
	296	distances <- Xwer_dist[,]
	297	rm(Xwer_dist) ; gc()
	298	distances #~small matrix K1 x K1
	299	}
	300
	301	# Helper function to divide indices into balanced sets
	302	# If max == TRUE, sets sizes cannot exceed nb_per_set
	303	.spreadIndices = function(indices, nb_per_set, max=FALSE)
	304	{
	305	L = length(indices)
	306	nb_workers = floor( L / nb_per_set )
	307	rem = L %% nb_per_set
	308	if (nb_workers == 0 \|\| (nb_workers==1 && rem==0))
	309	{
	310	# L <= nb_per_set, simple case
	311	indices_workers = list(indices)
	312	}
	313	else
	314	{
	315	indices_workers = lapply( seq_len(nb_workers), function(i)
	316	indices[(nb_per_set(i-1)+1):(nb_per_seti)] )
	317
	318	if (max)
	319	{
	320	# Sets are not so well balanced, but size is supposed to be critical
	321	return ( c( indices_workers, (L-rem+1):L ) )
	322	}
	323
	324	# Spread the remaining load among the workers
	325	rem = L %% nb_per_set
	326	while (rem > 0)
	327	{
	328	index = rem%%nb_workers + 1
	329	indices_workers[[index]] = c(indices_workers[[index]], indices[L-rem+1])
	330	rem = rem - 1
	331	}
	332	}
	333	indices_workers
	334	}