library("Rwave")

#precondition: ( log2(s0*w0/(2*pi)) - 1 ) * nvoice + 1.5 >= 1
toCWT  <- function(X, tw=0, swabs=0, nvoice=12, noctave=5, s0=2, w0=2*pi,
	spectra=FALSE, smooth=TRUE, scaled=FALSE, scalevector)
{
	if(missing(scalevector))
		scalevector  <- 2^(0:(noctave * nvoice) / nvoice) * s0
	s0log=as.integer((log2( s0*w0/(2*pi) )-1)*nvoice+1.5)
	totnoct=noctave+as.integer(s0log/nvoice)+1
	res <- lapply(1:nrow(X), function(n) {
		ts <- scale(ts( X[n,] ), 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)
		smat <- matrix(rep(sqs,length(t)),nrow=length(t),byrow=TRUE)
		ts.cwt*smat
	})
	if( spectra )
		res <- lapply(res, function(l) Mod(l)^2 )
	if( smooth  )
		res <- lapply(res, smCWT, swabs = swabs, tw = tw, scalevector = scalevector)
	resArray <- array(NA, c(nrow(res[[1]]), ncol(res[[1]]), length(res)))
	for( l in 1:length(res) )
		resArray[ , , l] <- res[[l]]
	resArray
}

#smooth cwt result
smCWT <- function(CWT, tw=  0, swabs= 0, nvoice= 12, noctave= 2, s0= 2, w0= 2*pi,
	lt= 24, scalevector )
{
	wsp     <- Mod(CWT)
	smwsp   <- smooth.matrix(wsp, swabs)
	smsmwsp <- smooth.time(smwsp, tw, scalevector)
	smsmwsp
}

#dans sowas.R (...donc on ne lisse pas à ce niveau ?)
smooth.matrix <- function(wt,swabs)
{
	if (swabs != 0)
	{
		smwt <- t(filter(t(wt),rep(1,2*swabs+1)/(2*swabs+1)))
	} else
	{
		smwt <- wt
	}
	smwt
}

smooth.time <- function(wt,tw,scalevector)
{
	smwt <- wt
	if (tw != 0)
	{
		for (i in 1:length(scalevector))
		{
			twi <- as.integer(scalevector[i]*tw)
			smwt[,i] <- filter(wt[,i],rep(1,2*twi+1)/(2*twi+1))
		}
	}
	smwt
}

#Entrée : courbes synchrones, soit après étape 1 itérée, soit après chaqure étape 1
step2 = function(conso)
{
	n     <- nrow(conso)
	m <- ncol(conso)

	#TODO: automatic tune of these parameters ? (for other users)
	nvoice   <- 4
	# noctave = 2^13 = 8192 half hours ~ 180 days ; ~log2(ncol(conso))
	noctave = 13
	# 4 here represent 2^5 = 32 half-hours ~ 1 day
	scalevector4  <- 2^(4:(noctave * nvoice) / nvoice) * 2
	lscvect4      <- length(scalevector4)
	lscvect <- lscvect4  # i should clean my code: werFam demands a lscvect

	# observations node with CWT
	Xcwt4   <- toCWT(conso, noctave = noctave, scalevector = scalevector4,
		smooth = FALSE, nvoice = nvoice)

	#matrix:
	Xcwt2 <- matrix(NA_complex_, nrow= n, ncol= 2 + length((c(Xcwt4[,,1]))))

	for(i in 1:n)
		Xcwt2[i,] <- c(m, lscvect, Xcwt4[,,i] / max(Mod(Xcwt4[,,i])) )

	rm(conso, Xcwt4) ; gc()

	lscvect = dim(Xcwt4)[2]

	Xwer_dist    <- matrix(0.0, n, n)
	for(i in 1:(n - 1))
	{
		mat1   <- matrix(as.vector(Xcwt2[i,])[-(1:2)], m, lscvect)

		for(j in (i + 1):n)
		{
			mat2 <- matrix(as.vector(Xcwt2[j,])[-(1:2)], m, lscvect)
			num     <- Mod(mat1 * Conj(mat2))
			WX      <- Mod(mat1 * Conj(mat1))
			WY      <- Mod(mat2 * Conj(mat2))
			smsmnum <- smCWT(num, scalevector = scalevector4)
			smsmWX  <- smCWT(WX,  scalevector = scalevector4)
			smsmWY  <- smCWT(WY,  scalevector = scalevector4)
			wer2    <- sum(colSums(smsmnum)^2)  /
				sum( sum(colSums(smsmWX) * colSums(smsmWY)) )
			Xwer_dist[i, j] <- sqrt(m * lscvect * (1 - wer2))
			Xwer_dist[j, i] <- Xwer_dist[i, j]
		}
	}
	diag(Xwer_dist) <- numeric(n)
	Xwer_dist
}