diff --git a/R/dlauricella.R b/R/dlauricella.R
new file mode 100644
index 0000000000000000000000000000000000000000..b06678780487d1bb0368d20eef2fa74581519199
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+++ b/R/dlauricella.R
@@ -0,0 +1,456 @@
+dlauricella <- function(nu1, nu2, lambda, eps = 1e-6) {
+
+ p <- length(lambda)
+
+ buildMlist <- function(j, isupp, k, k1, p = p) {
+ jsupp <- isupp[, j]
+ Ml <- rep(list(0:k), p)
+ for (j in jsupp)
+ Ml[[j]] <- k1
+ return(expand.grid(Ml))
+ }
+
+ buildxlist <- function(j, isupp, x, xsupp, p = p) {
+ jsupp <- isupp[, j]
+ xl <- rep(list(x), p)
+ xl[jsupp] <- xsupp[jsupp]
+ xl[-jsupp] <- x[-jsupp]
+ return(expand.grid(xl))
+ }
+
+ prodlambda <- prod(lambda)
+
+ lambdanu <- lambda*nu1/nu2
+ prodlambdanu <- prod(lambdanu)
+
+ k <- 5
+
+ # M: data.frame of the indices for the nested sums
+ # (i.e. all arrangements of n elements from {0:k})
+ M <- expand.grid(rep(list(0:k), p))
+ M <- M[-1, , drop = FALSE]
+
+ Munique <- 0:k
+
+ # Sum of the indices
+ Msum <- rowSums(M)
+ # Msumunique <- 0:max(Msum)
+
+ kstep <- 5
+
+ if (lambdanu[p] <= 1) { # lambda[1] < ... < lambda[p] < 1
+
+ if (p > 1 & lambda[p] == 1) {
+ lambda <- lambda[1:(p-1)]
+ p1 <- p-1
+ M <- expand.grid(rep(list(Munique), p1))
+ M <- M[-1, , drop = FALSE]
+ # Sum of the indices
+ Msum <- rowSums(M)
+ } else {
+ p1 <- p
+ }
+
+ Mpoch <- sapply(Munique, function(j) lnpochhammer(0.5, j))
+ matpoch <- matrix(rep(Mpoch, p1), ncol = p1, byrow = FALSE)
+ matM <- matrix(rep(Munique, p1), ncol = p1, byrow = FALSE)
+ matlabmda <- matrix(rep(log(1 - lambdanu[1:p1]), length(Munique)), ncol = p1, byrow = TRUE)
+ lambdaM <- matlabmda*matM
+ matfact <- matrix(rep(lfactorial(Munique), p1), ncol = p1, byrow = FALSE)
+
+ # matcommun <- exp(matpoch + lambdaM - matfact)
+ matcommun <- as.data.frame(matpoch + lambdaM - matfact)
+ # matcommun <- as.data.frame(apply(matcommun, 2, Re))
+ matcommunsupp <- as.data.frame(matrix(nrow = 0, ncol = ncol(matcommun)))
+ colnames(matcommunsupp) <- colnames(matcommun)
+
+ gridcommun <- expand.grid(matcommun)
+ gridcommun <- gridcommun[-1, , drop = FALSE]
+ # commun <- apply(gridcommun, 1, prod)
+ commun <- rowSums(gridcommun)
+
+ # d <- sum(
+ # commun * sapply(Msum, function(i) {
+ # pochhammer(1, i) / ( pochhammer((nu1 + p)/2, i) * i )
+ # })
+ # )
+ d <- Re(sum(exp(
+ commun + sapply(Msum, function(i) {
+ lnpochhammer(1, i) - ( lnpochhammer((nu1 + p)/2, i) + log(i) )
+ })
+ )))
+
+ # Next elements of the sum, until the expected precision
+ k1 <- 1:k
+ derive <- 0
+ while (abs(d) > eps/10 & !is.nan(d)) {
+ epsret <- signif(abs(d), 1)*10
+ k <- k1[length(k1)]
+ k1 <- k + (1:kstep)
+ derive <- derive + d
+
+ # M: data.frame of the indices for the nested sums
+ # M <- expand.grid(rep(list(k1), p1))
+ # if (p1 > 1) {
+ # for (i in 1:(p1-1)) {
+ # indsupp <- combn(p1, i)
+ # for (j in 1:ncol(indsupp)) {
+ # jsupp <- indsupp[, j]
+ # Mlist <- vector("list", p1)
+ # for (l in jsupp) Mlist[[l]] <- k1
+ # for (l in (1:p1)[-jsupp]) Mlist[[l]] <- 0:k
+ # M <- rbind(M, expand.grid(Mlist))
+ # }
+ # }
+ # }
+ Mlist <- list(expand.grid(rep(list(k1), p1)))
+ if (p1 == 1) {
+ M <- Mlist[[1]]
+ }
+ if (p1 > 1) {
+ for (i in 1:(p1-1)) {
+ indsupp <- combn(p1, i)
+ Mlist <- c(Mlist,
+ lapply(1:ncol(indsupp), buildMlist, isupp = indsupp, k = k, k1 = k1, p = p1))
+ }
+ M <- data.frame(rbindlist(Mlist))
+ }
+
+ # Sum of the indices
+ Msum <- rowSums(M)
+
+ Munique <- (max(Munique)+1):max(M)
+ # Msumunique <- (max(Msumunique)+1):max(Msum)
+
+ Mpoch <- sapply(Munique, function(j) lnpochhammer(0.5, j))
+ matpoch <- matrix(rep(Mpoch, p1), ncol = p1, byrow = FALSE)
+ matM <- matrix(rep(Munique, p1), ncol = p1, byrow = FALSE)
+ matlabmda <- matrix(rep(log(1 - lambdanu[1:p1]), length(Munique)), ncol = p1, byrow = TRUE)
+ lambdaM <- matlabmda*matM
+ matfact <- matrix(rep(lfactorial(Munique), p1), ncol = p1, byrow = FALSE)
+
+ matcommun <- rbind(matcommun, matcommunsupp)
+ # matcommunsupp <- exp(matpoch + lambdaM - matfact)
+ matcommunsupp <- as.data.frame(matpoch + lambdaM - matfact)
+ # matcommunsupp <- as.data.frame(apply(matcommunsupp, 2, Re))
+ colnames(matcommunsupp) <- colnames(matcommun)
+
+ communlist <- list(expand.grid(matcommunsupp))
+ if (p1 == 1) {
+ gridcommun <- communlist[[1]]
+ }
+ if (p1 > 1) {
+ for (i in 1:(p1-1)) {
+ indsupp <- combn(p1, i)
+ communlist <- c(communlist,
+ lapply(1:ncol(indsupp), buildxlist, isupp = indsupp, x = matcommun, xsupp = matcommunsupp, p = p1))
+ }
+ names(communlist[[1]]) <- names(communlist[[2]])
+ gridcommun <- data.frame(rbindlist(communlist))
+ }
+ # commun <- apply(gridcommun, 1, prod)
+ commun <- rowSums(gridcommun)
+
+ # d <- sum(
+ # commun * sapply(Msum, function(i) {
+ # pochhammer(1, i) / ( pochhammer((nu1 + p)/2, i) * i )
+ # })
+ # )
+ d <- Re(sum(exp(
+ commun + sapply(Msum, function(i) {
+ lnpochhammer(1, i) - ( lnpochhammer((nu1 + p)/2, i) + log(i) )
+ })
+ )))
+
+ }
+
+ derive <- as.numeric(-0.5 * log(prodlambda) - (nu2 + p)/2 * derive)
+
+ } else if (lambdanu[1] > 1) { # 1 < lambda[1] < ... < lambda[p]
+
+ Mpoch <- sapply(Munique, function(j) lnpochhammer(0.5, j))
+ matpoch <- matrix(rep(Mpoch, p), ncol = p, byrow = FALSE)
+ matM <- matrix(rep(Munique, p), ncol = p, byrow = FALSE)
+ matlabmda <- matrix(rep(log(1 - 1/lambdanu), length(Munique)), ncol = p, byrow = TRUE)
+ lambdaM <- matlabmda*matM
+ matfact <- matrix(rep(lfactorial(Munique), p), ncol = p, byrow = FALSE)
+
+ # matcommun <- exp(matpoch + lambdaM - matfact)
+ matcommun <- as.data.frame(matpoch + lambdaM - matfact)
+ # matcommun <- as.data.frame(apply(matcommun, 2, Re))
+ matcommunsupp <- as.data.frame(matrix(nrow = 0, ncol = ncol(matcommun)))
+ colnames(matcommunsupp) <- colnames(matcommun)
+
+ gridcommun <- expand.grid(matcommun)
+ gridcommun <- gridcommun[-1, , drop = FALSE]
+ # commun <- apply(gridcommun, 1, prod)
+ commun <- rowSums(gridcommun)
+
+ d <- 0
+ for (i in 1:length(Msum)) {
+ A <- sum(1/(0:(Msum[i]-1) + (nu1+p)/2))
+ d <- d - exp(commun[i]) * A
+ }
+ d <- Re(d)
+
+ # Next elements of the sum, until the expected precision
+ k1 <- 1:k
+ derive <- 0
+ # vd <- vderive <- numeric()
+ while (abs(d) > eps/10 & !is.nan(d)) {
+ epsret <- signif(abs(d), 1)*10
+ k <- k1[length(k1)]
+ k1 <- k + (1:kstep)
+ derive <- derive + d
+ # vd <- c(vd, d); vderive <- c(vderive, derive)
+
+ # # M: data.frame of the indices for the nested sums
+ # M <- as.data.frame(matrix(nrow = 0, ncol = p))
+ # if (p > 1) {
+ # for (i in 1:(p-1)) {
+ # Mlist <- c( rep(list(0:k), p-i), rep(list(k1), i) )
+ # M <- rbind( M, expand.grid(Mlist) )
+ # for (j in 1:(p-1)) {
+ # Mlist <- Mlist[c(p, 1:(p-1))]
+ # M <- rbind(M, expand.grid(Mlist))
+ # }
+ # }
+ # }
+ # M <- rbind( M, expand.grid(rep(list(k1), p)) )
+
+ # M: data.frame of the indices for the nested sums
+ # M <- expand.grid(rep(list(k1), p))
+ # if (p > 1) {
+ # for (i in 1:(p-1)) {
+ # indsupp <- combn(p, i)
+ # for (j in 1:ncol(indsupp)) {
+ # jsupp <- indsupp[, j]
+ # Mlist <- vector("list", p)
+ # for (l in jsupp) Mlist[[l]] <- k1
+ # for (l in (1:p)[-jsupp]) Mlist[[l]] <- 0:k
+ # M <- rbind(M, expand.grid(Mlist))
+ # }
+ # }
+ # }
+ Mlist <- list(expand.grid(rep(list(k1), p)))
+ if (p == 1) {
+ M <- Mlist[[1]]
+ }
+ if (p > 1) {
+ for (i in 1:(p-1)) {
+ indsupp <- combn(p, i)
+ Mlist <- c(Mlist,
+ lapply(1:ncol(indsupp), buildMlist, isupp = indsupp, k = k, k1 = k1, p = p))
+ }
+ M <- data.frame(rbindlist(Mlist))
+ }
+
+ Msum <- rowSums(M)
+
+ Munique <- (max(Munique) + 1):max(M)
+ # Msumunique <- (max(Msumunique) + 1):max(Msum)
+
+ # d <- 0
+ # for (i in 1:length(Msum)) {
+ # commun <- prod(
+ # sapply(1:p, function(j) {
+ # pochhammer(0.5, M[i, j])*(1 - 1/lambda[j])^M[i, j]/factorial(M[i, j])
+ # })
+ # )
+ # A <- sum(1/(0:(Msum[i]-1) + (1+p)/2))
+ # d <- d - commun * A # / pochhammer((1 + p)/2, Msum[i])
+ # }
+
+ Mpoch <- sapply(Munique, function(j) lnpochhammer(0.5, j))
+ matpoch <- matrix(rep(Mpoch, p), ncol = p, byrow = FALSE)
+ matM <- matrix(rep(Munique, p), ncol = p, byrow = FALSE)
+ matlabmda <- matrix(rep(log(1 - 1/lambdanu), length(Munique)), ncol = p, byrow = TRUE)
+ lambdaM <- matlabmda*matM
+ matfact <- matrix(rep(lfactorial(Munique), p), ncol = p, byrow = FALSE)
+
+ matcommun <- rbind(matcommun, matcommunsupp)
+ # matcommunsupp <- exp(matpoch + lambdaM - matfact)
+ matcommunsupp <- as.data.frame(matpoch + lambdaM - matfact)
+ # matcommunsupp <- as.data.frame(apply(matcommunsupp, 2, Re))
+ colnames(matcommunsupp) <- colnames(matcommun)
+
+ communlist <- list(expand.grid(matcommunsupp))
+ if (p == 1) {
+ gridcommun <- communlist[[1]]
+ }
+ if (p > 1) {
+ for (i in 1:(p-1)) {
+ indsupp <- combn(p, i)
+ communlist <- c(communlist,
+ lapply(1:ncol(indsupp), buildxlist, isupp = indsupp, x = matcommun, xsupp = matcommunsupp, p = p))
+ }
+ names(communlist[[1]]) <- names(communlist[[2]])
+ gridcommun <- data.frame(rbindlist(communlist))
+ }
+ # commun <- apply(gridcommun, 1, prod)
+ commun <- rowSums(gridcommun)
+
+ # d <- 0
+ # for (i in 1:length(Msum)) {
+ # A <- sum(1/(0:(Msum[i]-1) + (1+p)/2))
+ # d <- d - commun[i] * A
+ # }
+ A <- sapply(Msum, function (i) sum(1/(0:(i-1) + (nu1+p)/2)))
+
+ d <- Re(-sum(exp(commun)*A))
+
+ }
+
+ derive <- as.numeric(-0.5 * log(prodlambda) - (nu2 + p)/2 * prod(1/sqrt(lambdanu)) * derive)
+
+ } else { # lambda[1] < ... < 1 < ... < lambda[p]
+
+ Mpoch <- sapply(Munique, function(j) lnpochhammer(0.5, j))
+ matpoch <- cbind(matrix(rep(Mpoch, p-1), ncol = p-1, byrow = FALSE), 0)
+ matM <- matrix(rep(Munique, p), ncol = p, byrow = FALSE)
+ matlabmda <- matrix(rep(log(1 - c(lambdanu[-p], 1)/lambdanu[p]), length(Munique)), ncol = p, byrow = TRUE)
+ lambdaM <- matlabmda*matM
+ matfact <- matrix(rep(lfactorial(Munique), p), ncol = p, byrow = FALSE)
+
+ # matcommun <- exp(matpoch + lambdaM - matfact)
+ matcommun <- as.data.frame(matpoch + lambdaM - matfact)
+ # matcommun <- as.data.frame(apply(matcommun, 2, Re))
+ matcommunsupp <- as.data.frame(matrix(nrow = 0, ncol = ncol(matcommun)))
+ colnames(matcommunsupp) <- colnames(matcommun)
+
+ gridcommun <- expand.grid(matcommun)
+ gridcommun <- gridcommun[-1, , drop = FALSE]
+ # commun <- apply(gridcommun, 1, prod)
+ commun <- rowSums(gridcommun)
+
+ # d <- sum(
+ # commun * sapply(1:length(Msum), function(i) {
+ # pochhammer(0.5, M[i, p]) * pochhammer(1, Msum[i]) / ( pochhammer((nu1 + p)/2, Msum[i]) * Msum[i] )
+ # })
+ # )
+ d <- Re(sum(exp(
+ commun + sapply(1:length(Msum), function(i) {
+ lnpochhammer(0.5, M[i, p]) + lnpochhammer(1, Msum[i]) -
+ ( lnpochhammer((nu1 + p)/2, Msum[i]) + log(Msum[i]) )
+ })
+ )))
+
+ # Next elements of the sum, until the expected precision
+ k1 <- 1:k
+ derive <- 0
+ while (abs(d) > eps/10 & !is.nan(d)) {
+ epsret <- signif(abs(d), 1)*10
+ k <- k1[length(k1)]
+ k1 <- k + (1:kstep)
+ derive <- derive + d
+
+ # # M: data.frame of the indices for the nested sums
+ # M <- as.data.frame(matrix(nrow = 0, ncol = p))
+ # if (p > 1) {
+ # for (i in 1:(p-1)) {
+ # Mlist <- c( rep(list(0:k), p-i), rep(list(k1), i) )
+ # M <- rbind( M, expand.grid(Mlist) )
+ # for (j in 1:(p-1)) {
+ # Mlist <- Mlist[c(p, 1:(p-1))]
+ # M <- rbind(M, expand.grid(Mlist))
+ # }
+ # }
+ # }
+ # M <- rbind( M, expand.grid(rep(list(k1), p)) )
+
+ # M <- expand.grid(rep(list(k1), p))
+ # if (p > 1) {
+ # for (i in 1:(p-1)) {
+ # indsupp <- combn(p, i)
+ # for (j in 1:ncol(indsupp)) {
+ # jsupp <- indsupp[, j]
+ # Mlist <- vector("list", p)
+ # for (l in jsupp) Mlist[[l]] <- k1
+ # for (l in (1:p)[-jsupp]) Mlist[[l]] <- 0:k
+ # M <- rbind(M, expand.grid(Mlist))
+ # }
+ # }
+ # }
+
+ # M: data.frame of the indices for the nested sums
+ Mlist <- list(expand.grid(rep(list(k1), p)))
+ if (p == 1) {
+ M <- Mlist[[1]]
+ }
+ if (p > 1) {
+ for (i in 1:(p-1)) {
+ indsupp <- combn(p, i)
+ Mlist <- c(Mlist,
+ lapply(1:ncol(indsupp), buildMlist, isupp = indsupp, k = k, k1 = k1, p = p))
+ }
+ M <- data.frame(rbindlist(Mlist))
+ }
+
+ Msum <- rowSums(M)
+
+ Munique <- (max(Munique)+1):max(M)
+ # Msumunique <- (max(Msumunique)+1):max(Msum)
+
+ # d <- 0
+ # for (i in 1:length(Msum)) {
+ # commun <- prod(
+ # sapply(1:(p-1), function(j) {
+ # pochhammer(0.5, M[i, j])*(1 - lambda[j]/lambda[p])^M[i, j]/factorial(M[i, j])
+ # })
+ # )
+ # commun <- commun*(1 - 1/lambda[p])^M[i, p]/factorial(M[i, p])
+ # d <- d + commun * pochhammer(0.5, M[i, p])*pochhammer(1, Msum[i]) / ( pochhammer((1 + p)/2, Msum[i]) * Msum[i] )
+ # }
+
+ Mpoch <- sapply(Munique, function(j) lnpochhammer(0.5, j))
+ matpoch <- cbind(matrix(rep(Mpoch, p-1), ncol = p-1, byrow = FALSE), 0)
+ matM <- matrix(rep(Munique, p), ncol = p, byrow = FALSE)
+ matlabmda <- matrix(rep(log(1 - c(lambdanu[-p], 1)/lambdanu[p]), length(Munique)), ncol = p, byrow = TRUE)
+ lambdaM <- matlabmda*matM
+ matfact <- matrix(rep(lfactorial(Munique), p), ncol = p, byrow = FALSE)
+
+ matcommun <- rbind(matcommun, matcommunsupp)
+ # matcommunsupp <- exp(matpoch + lambdaM - matfact)
+ matcommunsupp <- as.data.frame(matpoch + lambdaM - matfact)
+ # matcommunsupp <- as.data.frame(apply(matcommunsupp, 2, Re))
+ colnames(matcommunsupp) <- colnames(matcommun)
+
+ communlist <- list(expand.grid(matcommunsupp))
+ if (p == 1) {
+ gridcommun <- communlist[[1]]
+ }
+ if (p > 1) {
+ for (i in 1:(p-1)) {
+ indsupp <- combn(p, i)
+ communlist <- c(communlist,
+ lapply(1:ncol(indsupp), buildxlist, isupp = indsupp, x = matcommun, xsupp = matcommunsupp, p = p))
+ }
+ names(communlist[[1]]) <- names(communlist[[2]])
+ gridcommun <- data.frame(rbindlist(communlist))
+ }
+ commun <- apply(gridcommun, 1, prod)
+ commun <- rowSums(gridcommun)
+
+ # d <- sum(
+ # commun * sapply(1:length(Msum), function(i) {
+ # pochhammer(0.5, M[i, p]) * pochhammer(1, Msum[i]) / ( pochhammer((nu1 + p)/2, Msum[i]) * Msum[i] )
+ # })
+ # )
+ d <- Re(sum(exp(
+ commun + sapply(1:length(Msum), function(i) {
+ lnpochhammer(0.5, M[i, p]) + lnpochhammer(1, Msum[i]) -
+ ( lnpochhammer((nu1 + p)/2, Msum[i]) + log(Msum[i]) )
+ })
+ )))
+
+ }
+
+ derive <- as.numeric(-0.5 * log(prodlambda) + (nu2 + p)/2 * (log(lambdanu[p]) - derive))
+
+ }
+
+ attr(derive, "epsilon") <- eps
+ attr(derive, "k") <- k
+
+ return(derive)
+}