R/pmlMix.R

In phangorn: Phylogenetic Reconstruction and Analysis

logLik_pmlMix <- function(fits, weight, omega){
  res <- NULL
  for(i in 1:length(omega)){
    res <- fits[[1]]$ll.0 * omega[i]
  }
  sum(log(res)*weight)
}


optimMixQ <- function(object, Q = c(1, 1, 1, 1, 1, 1), omega, ...) {
  l <- length(Q)
  Q <- Q[-l]
  Q <- sqrt(Q)
  fn <- function(Q, object, omega, ...) {
    Q <- c(Q^2, 1)
    weight <- object[[1]]$weight
    n <- length(omega)
    p <- length(weight)
    result <- numeric(p)
    for (i in 1:n) result <- result +
        as.numeric(update(object[[i]], Q = Q)$lv) * omega[i]
    res <- sum(weight * log(result))
    res
  }
  res <- optim(par = Q, fn = fn, gr = NULL, method = "L-BFGS-B", lower = 0,
    upper = Inf, control = list(fnscale = -1, maxit = 25),
    object = object, omega = omega, ...)
  res[[1]] <- c(res[[1]]^2, 1)
  res
}


optimMixM1a <- function(object, dnds = 0.1, omega, scaleQ = 1, ...) {
  weight <- object[[1]]$weight
  l0 <- object[[2]]$lv * omega[2]
  fn <- function(dnds, object, omega, weight, l0, scaleQ, ...) {
    result <- l0 +
      as.numeric(update(object, dnds = dnds, scaleQ = scaleQ, ...)$lv) *
      omega[1]
    sum(weight %*% log(result))
  }
  res <- optimize(f = fn, c(0, 1), object = object[[1]], omega = omega,
    weight = weight, l0 = l0, scaleQ = scaleQ, lower = 0, upper = 1,
    maximum = TRUE)
  res
}


optimMixM2a <- function(object, dnds_old = c(0.1, 2), omega, scaleQ = 1, ...) {
  weight <- object[[1]]$weight
  l2 <- object[[2]]$lv * omega[2]
  fn <- function(dnds, object, omega, weight, l0, scaleQ, ...) {
    result <- l0 +
      as.numeric(update(object, dnds = dnds, scaleQ = scaleQ, ...)$lv) *
      omega[1]
    sum(weight %*% log(result))
  }
  l3  <- object[[3]]$lv * omega[3]
  dnds <- dnds_old
  for (i in 1:3) {
    res <- optimize(f = fn, c(0, 1), object = object[[1]], omega = omega,
      weight = weight, l0 = l2 + l3, scaleQ = scaleQ,
      lower = 0, upper = 1, maximum = TRUE)
    dnds[1] <- res[[1]]
    l1 <- update(object[[1]], dnds = res[[1]], scaleQ = scaleQ)$lv * omega[1]
    res <- optimize(f = fn, c(1, 10), object = object[[3]], omega = omega,
      weight = weight, l0 = l2 + l1, scaleQ = scaleQ,
      lower = 1, upper = 10, maximum = TRUE)
    dnds[2] <- res[[1]]
    l3 <- update(object[[3]], dnds = res[[1]], scaleQ = scaleQ)$lv * omega[3]
  }
  dnds
}


optimMixM7 <- function(object, pq = c(1, 1), omega, scaleQ = 1, ...) {
  weight <- object[[1]]$weight

  fn <- function(pq, object, omega, weight, scaleQ, ...) {
    dnds <- discrete.beta(pq[1], pq[2], length(omega))
    result <- numeric(length(weight))
    for (i in seq_along(omega)) result <- result +
        as.numeric(update(object[[i]], dnds = dnds[i],
                          scaleQ = scaleQ, ...)$lv) * omega[i]
    sum(weight %*% log(result))
  }
  res <- optimize(f = fn, c(1, 1), object = object[[1]], omega = omega,
    weight = weight, scaleQ = scaleQ,
    lower = c(0, 0), upper = c(10, 10), maximum = TRUE)
  res
}


# needs to be included
optimMixTSTV <- function(object, tstv = 1, omega, scaleQ = 1, ...) {
  weight <- object[[1]]$weight
  fn <- function(tstv, object, omega, weight, scaleQ, ...) {
    result <- numeric(length(weight))
    for (i in seq_along(omega)) result <- result +
      as.numeric(update(object[[i]], tstv = tstv, scaleQ = scaleQ, ...)$lv) *
        omega[i]
    sum(weight %*% log(result))
  }
  res <- optimize(f = fn, c(0, 100), object = object, omega = omega,
    weight = weight, scaleQ=scaleQ, lower = 0, upper = 100, maximum = TRUE)
  res
}


optimAllRate <- function(object, rate = 1, omega, ...) {
  weight <- object[[1]]$weight
  fn <- function(rate, object, omega, weight, ...) {
    result <- numeric(length(weight))
    for (i in seq_along(object)) result <- result +
        as.numeric(update(object[[i]], rate = rate, ...)$lv) *
        omega[i]
    sum(weight %*% log(result))
  }
  res <- optimize(f = fn, c(0.01, 10), object = object, omega = omega,
                  weight = weight, lower = 0.01, upper = 10, maximum = TRUE)
  res
}



optimMixBf <- function(object, bf = c(.25, .25, .25, .25), omega, ...) {
  l <- length(bf)
  nenner <- 1 / bf[l]
  lbf <- log(bf * nenner)
  lbf <- lbf[-l]
  fn <- function(lbf, object, omega, ...) {
    bf <- exp(c(lbf, 0))
    bf <- bf / sum(bf)
    weight <- object[[1]]$weight
    p <- length(weight)
    result <- numeric(p)
    for (i in seq_along(omega)) result <- result +
        as.numeric(update(object[[i]], bf = bf)$lv) * omega[i]
    result <- sum(weight * log(result))
    result
  }
  res <- optim(par = lbf, fn = fn, gr = NULL, method = "Nelder-Mead",
    control = list(fnscale = -1, maxit = 500), object, omega = omega, ...)
  bf <- exp(c(res[[1]], 0))
  bf <- bf / sum(bf)
}


optimMixInv <- function(object, inv = 0.01, omega, ...) {
  fn <- function(inv, object, omega){ #, ...) {
    weight <- as.vector(object[[1]]$weight)
    p <- length(weight)
    result <- numeric(p)
    for (i in seq_along(omega)) result <- result +
        update(object[[i]], inv = inv)$lv * omega[i]
    res <- sum(weight * log(result))
    res
  }
  res <- optimize(f = fn, interval = c(0, 1), lower = 0, upper = 1,
                  maximum = TRUE, tol = .0001, object, omega = omega, ...)
  res[[1]]
}



optimMixRate <- function(fits, ll, weight, omega, rate = rep(1, length(fits))) {
  r <- length(fits)
  rate0 <- c(rate[1], diff(rate))
  rate0[rate0 < 1e-8] <- 1e-8 # required by constrOptim
  R <- matrix(0, r, r)
  R[lower.tri(R, TRUE)] <- 1
  fn <- function(rate, fits, ll, weight, omega, R) {
    rate <- as.vector(R %*% rate)
    r <-  length(rate)
    for (i in 1:r) fits[[i]] <- update(fits[[i]], rate = rate[i])
    for (i in 1:r) ll[, i] <- fits[[i]]$lv
    sum(weight * log(ll %*% omega))
  }
  ui <- rbind(R, diag(r))
  ci <- rep(0, 2 * r)
  # Maybe constrain rates * omega
  res <- constrOptim(rate0, fn, grad = NULL, ui = ui, ci = ci, mu = 1e-04,
                     control = list(fnscale = -1), method = "Nelder-Mead",
                     outer.iterations = 100, outer.eps = 1e-08, fits = fits,
                     ll = ll, weight = weight, omega = omega, R=R)
  rate <- res[[1]]
  res[[1]] <- as.vector(R %*% rate)
  res
}


optW <- function(ll, weight, omega, eps=1e-8, ...) {
  k <- length(omega)
  nenner <- 1 / omega[1]
  eta <- log(omega * nenner)
  eta <- eta[-1]
  fn <- function(eta, ll, weight) {
    eta <- c(0, eta)
    p <- exp(eta) / sum(exp(eta))
    res <- sum(weight * log(ll %*% p))
    res
  }
  start <- fn(eta, ll, weight)
  if (k == 2) res <- optimize(f = fn, interval = c(-3, 3), lower = -3,
                              upper = 3, maximum = TRUE,
                              tol = .Machine$double.eps^0.25, ll = ll,
                              weight = weight)
  else res <- optim(eta, fn = fn, method = "L-BFGS-B", lower = -5, upper = 5,
                    control = list(fnscale = -1, maxit = 25), gr = NULL,
                    ll = ll, weight = weight)
  p <- exp(c(0, res[[1]]))
  p <- p / sum(p)
  if(((res[[2]] - start) / abs(start)) < eps) {
    result <- list(par = omega, value = start, start=start)
  } else  result <- list(par = p, value = res[[2]], start=start)
  result
}


optimMixEdge <- function(object, omega, trace = 1, ...) {
  tree <- object[[1]]$tree
  theta <- object[[1]]$tree$edge.length
  weight <- as.numeric(attr(object[[1]]$data, "weight"))
  n <- length(omega)
  p <- length(weight)
  q <- length(theta)
  lv1 <- numeric(p)
  for (i in 1:n) lv1 <- lv1 + as.numeric(object[[i]]$lv) * omega[i]
  ll0 <- sum(weight * log(lv1))
  eps <- 1
  iter <- 0
  scalep <- 1
  if (trace > 0) cat(ll0)
  while (abs(eps) > .0001 & iter < 10) {
    dl <- matrix(0, p, q)
    for (i in 1:n) dl <- dl + dl(object[[i]], TRUE) * omega[i]
    dl <- dl / lv1
    sc <- colSums(weight * dl)
    F <- crossprod(dl * weight, dl) + diag(q) * 1e-6
    blub <- TRUE
    iter2 <- 0
    while (blub & iter2 < 10) {
      thetaNew <- log(theta) + scalep * solve(F, sc)
      tree$edge.length <- as.numeric(exp(thetaNew))
      for (i in 1:n) object[[i]] <- update(object[[i]], tree = tree)
      lv1 <- numeric(p)
      for (i in 1:n) lv1 <- lv1 + as.numeric(object[[i]]$lv)  * omega[i]
      ll1 <- sum(weight * log(lv1))
      eps <- ll1 - ll0
      if (eps < 0 || is.nan(eps)) {
        scalep <- scalep / 2
        eps <- 1
        thetaNew <- log(theta)
        ll1 <- ll0
        iter2 <- iter2 + 1
      }
      else {
        scalep <- 1
        theta <- exp(thetaNew)
        blub <- FALSE
      }
    }
    iter <- iter + 1
    ll0 <- ll1
  }
  tree$edge.length <- theta
  for (i in 1:n) object[[i]] <- update(object[[i]], tree = tree)
  if (trace > 0) cat("->", ll1, "\n")
  object
}


#' Phylogenetic mixture model
#'
#' Phylogenetic mixture model.
#'
#' The \code{formula} object allows to specify which parameter get optimized.
#' The formula is generally of the form \code{edge + bf + Q ~ rate + shape +
#' \dots{}}, on the left side are the parameters which get optimized over all
#' mixtures, on the right the parameter which are optimized specific to each
#' mixture. The parameters available are \code{"nni", "bf", "Q", "inv",
#' "shape", "edge", "rate"}.  Each parameters can be used only once in the
#' formula.  \code{"rate"} and \code{"nni"} are only available for the right
#' side of the formula. On the other hand parameters for invariable sites are
#' only allowed on the left-hand side.  The convergence of the algorithm is
#' very slow and is likely that the algorithm can get stuck in local optima.
#'
#' @aliases pmlMix
#' @param formula a formula object (see details).
#' @param fit an object of class \code{pml}.
#' @param m number of mixtures.
#' @param omega mixing weights.
#' @param control A list of parameters for controlling the fitting process.
#' @param \dots Further arguments passed to or from other methods.
#' @return \code{pmlMix} returns a list with elements
#' \item{logLik}{log-likelihood of the fit} \item{omega}{mixing weights.}
#' \item{fits}{fits for the final mixtures.}
#' @author Klaus Schliep \email{klaus.schliep@@gmail.com}
#' @seealso \code{\link{pml}},\code{\link{pmlPart}},\code{\link{pmlCluster}}
#' @keywords cluster
#' @examples
#'
#' \dontrun{
#' X <- allSitePattern(5)
#' tree <- read.tree(text = "((t1:0.3,t2:0.3):0.1,(t3:0.3,t4:0.3):0.1,t5:0.5);")
#' fit <- pml(tree,X, k=4)
#' weights <- 1000*exp(fit$siteLik)
#' attr(X, "weight") <- weights
#' fit1 <- update(fit, data=X, k=1)
#' fit2 <- update(fit, data=X)
#'
#' (fitMixture <- pmlMix(edge~rate, fit1 , m=4))
#' (fit2 <- optim.pml(fit2, optGamma=TRUE))
#'
#'
#' data(Laurasiatherian)
#' dm <- dist.logDet(Laurasiatherian)
#' tree <- NJ(dm)
#' fit <- pml(tree, Laurasiatherian)
#' fit <- optim.pml(fit)
#'
#' fit2 <- update(fit, k=4)
#' fit2 <- optim.pml(fit2, optGamma=TRUE)
#'
#' fitMix <- pmlMix(edge ~ rate, fit, m=4)
#' fitMix
#'
#'
#' #
#' # simulation of mixture models
#' #
#' X <- allSitePattern(5)
#' tree1 <- read.tree(text = "((t1:0.1,t2:0.5):0.1,(t3:0.1,t4:0.5):0.1,t5:0.5);")
#' tree2 <- read.tree(text = "((t1:0.5,t2:0.1):0.1,(t3:0.5,t4:0.1):0.1,t5:0.5);")
#' tree1 <- unroot(tree1)
#' tree2 <- unroot(tree2)
#' fit1 <- pml(tree1,X)
#' fit2 <- pml(tree2,X)
#'
#' weights <- 2000*exp(fit1$siteLik) + 1000*exp(fit2$siteLik)
#' attr(X, "weight") <- weights
#'
#' fit1 <- pml(tree1, X)
#' fit2 <- optim.pml(fit1)
#' logLik(fit2)
#' AIC(fit2, k=log(3000))
#'
#' fitMixEdge <- pmlMix( ~ edge, fit1, m=2)
#' logLik(fitMixEdge)
#' AIC(fitMixEdge, k=log(3000))
#'
#' fit.p <- pmlPen(fitMixEdge, .25)
#' logLik(fit.p)
#' AIC(fit.p, k=log(3000))
#' }
#'
#' @export pmlMix
pmlMix <- function(formula, fit, m = 2, omega = rep(1 / m, m),
                   control = pml.control(epsilon = 1e-8, maxit = 20, trace = 1),
                   ...) {
  call <- match.call()
  form <- phangornParseFormula(formula)
  opt <- c("nni", "bf", "Q", "inv", "shape", "edge", "rate", "M1a", "M2a")
  optAll <- match(opt, form$left)
  optPart <- match(opt, form$right)
  AllBf <- !is.na(optAll[2])
  AllQ <- !is.na(optAll[3])
  AllInv <- !is.na(optAll[4])
  AllGamma <- !is.na(optAll[5])
  AllEdge <- !is.na(optAll[6])
  AllRate <- !is.na(optAll[7])
  MixNni <- !is.na(optPart[1])
  if(MixNni) MixEdge <- TRUE
  MixBf <- !is.na(optPart[2])
  MixQ <- !is.na(optPart[3])
  MixInv <- !is.na(optPart[4])
  MixGamma <- !is.na(optPart[5])
  MixEdge <- !is.na(optPart[6])
  MixRate <- !is.na(optPart[7])
  M1a <- !is.na(optPart[8])
  M2a <- !is.na(optPart[9])
  if (inherits(fit, "pmlMix")){
    fits <- fit$fits
    omega <- fit$omega
  }
  if (inherits(fit, "list")){
    fits <- fit
    m <- length(fits)
    if(length(omega) != m) omega <- rep(1 / m, m)
  }
  if (inherits(fit, "pml")) {
    fits <- vector("list", m)
    for (i in 1:m) fits[[i]] <- fit
  }
  dat <- fits[[1]]$data
  p <- attr(dat, "nr")
  weight <- attr(dat, "weight")
  r <- m
  ll <- matrix(0, p, r)
  for (i in 1:r) ll[, i] <- fits[[i]]$lv

  for (i in 1:r) {
    pl0 <- ll[, -i, drop = FALSE] %*% omega[-i]
    fits[[i]] <- update(fits[[i]], llMix = pl0, wMix = omega[i])
  }
  if (MixRate) rate <- rep(1, r)
  dnds <- NULL
  CODON <- FALSE
  if (M1a) {
    dnds <- c(fits[[1]]$dnds, fits[[2]]$dnds)
    CODON <- TRUE
    codon <- "M1a"
  }
  if (M2a) {
    dnds <- c(fits[[1]]$dnds, 1, fits[[3]]$dnds)
    CODON <- TRUE
    codon <- "M2a"
  }

  llstart <- sum(weight * log(ll %*% omega))
  llold <- llstart
  ll_tmp <- llstart
  ll3 <- ll1 <- llstart
  eps0 <- 1
  iter0 <- 0
  trace <- control$trace

  on.exit({
    parameter <- c(AllBf = AllBf, AllQ = AllQ, AllInv = AllInv,
                   AllGamma = AllGamma, AllEdge = AllEdge, MixNni = MixNni,
                   MixBf = MixBf, MixQ = MixQ, MixInv = MixInv,
                   MixGamma = MixGamma, MixEdge = MixEdge, MixRate = MixRate)
    df <- matrix(1, 6, 2)
    colnames(df) <- c("#df", "group")
    rownames(df) <- c("Edge", "Shape", "Inv", "Bf", "Q", "Rate")
    df[1, 1] <- length(fits[[1]]$tree$edge.length)
    df[2, 1] <- fits[[1]]$k > 1
    df[3, 1] <- fits[[1]]$inv > 0
    df[4, 1] <- length(unique(fits[[1]]$bf)) - 1
    df[5, 1] <- length(unique(fits[[1]]$Q)) - 1
    df[6, 1] <- 0
    if (MixEdge) df[1, 2] <- r
    if (MixGamma) df[2, 2] <- r
    if (MixInv) df[3, 2] <- r
    if (MixBf) df[4, 2] <- r
    if (MixQ) df[5, 2] <- r
    if (MixRate) df[6, 1] <- r - 1
    attr(logLik, "df") <- sum(df[, 1] * df[, 2])
    converge <- c(iter = iter0, eps = eps0)
    if (CODON){
      if(M1a) df[5,1] <- 3
      if(M2a) df[5,1] <- 5
      df[4, 1] <- df_freq_codon(fits[[1]]$frequencies)
      result <- list(logLik = ll1, omega = omega, fits = fits, call = call,
                     converge = converge, parameter = parameter, df = df,
                     dnds = dnds, codon = codon)
    }
    else
      result <- list(logLik = ll1, omega = omega, fits = fits, call = call,
                     converge = converge, parameter = parameter, df = df)
    class(result) <- "pmlMix"
    return(result)
  })


  while (eps0 > control$eps & iter0 < control$maxit) {
    eps1 <- 100
    iter1 <- 0

    if (AllQ) {
      newQ <- optimMixQ(fits, Q = fits[[1]]$Q, omega = omega)[[1]]
      for (i in seq_len(m)) fits[[i]] <- update(fits[[i]], Q = newQ)
    }
    if (AllBf) {
      newBf <- optimMixBf(fits, bf = fits[[1]]$bf,
        omega = omega)
      for (i in seq_len(m)) fits[[i]] <- update(fits[[i]], bf = newBf)
    }
    if (AllInv) {
      newInv <- optimMixInv(fits, inv = fits[[1]]$inv,
        omega = omega)
      for (i in seq_len(m)) fits[[i]] <- update(fits[[i]], inv = newInv)
    }
    if (AllRate) {
      newrate <- optimAllRate(fits, rate=1, omega)
      for (i in  seq_len(m)) fits[[i]] <- update(fits[[i]], rate = newrate[[1]])
    }
    if (M1a) {
      tmp <- optimMixM1a(fits, dnds[1], omega, scaleQ = 1)
      fits[[1]] <- update(fits[[1]], dnds = tmp[[1]], scaleQ = 1)
      dnds[1] <- tmp[[1]]
      ll[, 1] <- fits[[1]]$lv
    }
    if (M2a) {
      tmp <- optimMixM2a(fits, dnds[c(1, 3)], omega, scaleQ = 1) # [[1]]
      fits[[1]] <- update(fits[[1]], dnds = tmp[1], scaleQ = 1)
      fits[[3]] <- update(fits[[3]], dnds = tmp[2], scaleQ = 1)
      dnds[c(1, 3)] <- tmp
    }
    if (CODON) {
      tstv <- fits[[2]]$tstv
      tmp <- optimMixTSTV(fits, tstv, omega, scaleQ = 1)
      for (i in seq_len(m)) {
        fits[[i]] <- update(fits[[i]], tstv = tmp[[1]], scaleQ = 1)
      }
      tstv <- tmp[[1]]
    }
    if (AllEdge)
      fits <- optimMixEdge(fits, omega, trace = trace - 1)
    for (i in 1:r) ll[, i] <- fits[[i]]$lv

    if (MixRate) {
      res <- optimMixRate(fits, ll, weight, omega, rate)
      if(res[[2]] > ll1){
        rate <- res[[1]]
        blub <- sum(rate * omega)
        rate <- rate / blub
        tree <- fits[[1]]$tree
        tree$edge.length <- tree$edge.length * blub
        for (i in 1:r) fits[[i]] <- update(fits[[i]], tree = tree,
                                           rate = rate[i])
        for (i in 1:r) ll[, i] <- fits[[i]]$lv
        if (trace > 0) cat("optimize rates: ", ll1, "-->", res[[2]],
                           "\n rates", rate, "\n")
        ll1 <- res[[2]]
      }
    }
    if (any(c(MixNni, MixBf, MixQ, MixInv, MixGamma, MixEdge))) {
      while (abs(eps1) > 0.001 & iter1 < 3) {
        for (i in 1:r) {
          pl0 <- ll[, -i, drop = FALSE] %*% omega[-i]
          fits[[i]] <- update(fits[[i]], llMix = pl0, wMix = omega[i])
        }
        if(trace >0) cat("logLik optim.pml start:", sum(weight * log(ll %*% omega)), "\n")
        for (i in 1:r) {
          pl0 <- ll[, -i, drop = FALSE] %*% omega[-i]
          fits[[i]] <- optim.pml(fits[[i]], optNni = MixNni, optBf = MixBf,
                            optQ = MixQ, optInv = MixInv, optGamma = MixGamma,
                            optEdge = MixEdge, optRate = FALSE,
                            control = pml.control(epsilon = 1e-8, maxit = 3,
                            trace - 1), llMix = pl0, wMix = omega[i])
          ll[, i] <- fits[[i]]$lv

          if(trace >0) cat("logLik optim.pml", i, ": ", sum(weight * log(ll %*% omega)), "\n")
#          res <- optW(ll, weight, omega)
#          omega <- res$p
          if (MixRate) {
            blub <- sum(rate * omega)
            rate <- rate / blub
            tree <- fits[[1]]$tree
            tree$edge.length <- tree$edge.length * blub
            for (j in 1:r){
              fits[[j]] <- update(fits[[j]], tree = tree, rate = rate[j])
              ll[, j] <- fits[[j]]$lv
            }
          }
#          for (j in 1:r) {
#            pl0 <- ll[, -j, drop = FALSE] %*% omega[-j]
#            fits[[j]] <- update(fits[[j]], llMix = pl0, wMix = omega[j])
#          }
        }
        res <- optW(ll, weight, omega)
        omega <- res$p
#        for (j in 1:r){
#          fits[[j]] <- update(fits[[j]], tree = tree, rate = rate[j])
#          ll[, j] <- fits[[j]]$lv
#        }
        for (j in 1:r) {
          pl0 <- ll[, -j, drop = FALSE] %*% omega[-j]
          fits[[j]] <- update(fits[[j]], llMix = pl0, wMix = omega[j])
        }


        ll2 <- sum(weight * log(ll %*% omega))
        eps1 <- llold - ll2
        iter1 <- iter1 + 1
        llold <- ll2
        }
      }

      res <- optW(ll, weight, omega)
      omega <- res$p
      if (MixRate) {
        blub <- sum(rate * omega)
        rate <- rate / blub
        tree <- fits[[1]]$tree
        tree$edge.length <- tree$edge.length * blub
        for (i in 1:r) fits[[i]] <- update(fits[[i]], tree = tree,
                                           rate = rate[i])
        for (i in 1:r) ll[, i] <- fits[[i]]$lv
      }
      for (i in 1:r) {
        pl0 <- ll[, -i, drop = FALSE] %*% omega[-i]
        fits[[i]] <- update(fits[[i]], llMix = pl0, wMix = omega[i])
      }


    ll1 <- sum(weight * log(ll %*% omega))
    eps0 <- (ll3 - ll1) / ll1
    iter0 <- iter0 + 1
    if (trace > 0) {
      cat("iteration:", iter0, "\n")
      cat("omega:", omega, "\n")
      cat("log-likelihood:", ll3, "==>", ll1, "\n")
    }
    ll3 <- ll1
  }
}

#' @export
print.pmlMix <- function(x, ...) {
  nc <- attr(x$fits[[1]]$data, "nc")
  nr <- attr(x$fits[[1]]$data, "nr")
  levels <- attr(x$fits[[1]]$data, "levels")
  r <- length(x$fits)
  w <- x$fits[[1]]$weight
  w <- w[w > 0]
  type <- attr(x$fits[[1]]$data, "type")
  nc <- attr(x$fits[[1]]$data, "nc")
  ll0 <- sum(w * log(w / sum(w)))
  bf <- matrix(0, r, nc)
  dimnames(bf) <- list(1:r, levels)
  Q <- matrix(0, r, nc * (nc - 1) / 2)
  dimnames(Q) <- list(1:r, NULL)

  rate <- numeric(r)
  inv <- numeric(r) # x$fits[[1]]$inv
  shape <- numeric(r)

  for (i in 1:r) {
    bf[i, ] <- x$fits[[i]]$bf
    Q[i, ] <- x$fits[[i]]$Q
    rate[i] <- x$fits[[i]]$rate
    shape[i] <- x$fits[[i]]$shape
    inv[i] <- x$fits[[i]]$inv
  }
  cat("\nloglikelihood:", x$logLik, "\n")
  cat("\nunconstrained loglikelihood:", ll0, "\n")
  cat("AIC: ", AIC(x), " BIC: ", AIC(x, k = log(nr)), "\n\n")
  cat("\nposterior:", x$omega, "\n")
  if (any(inv > 0)) cat("Proportion of invariant sites:", inv, "\n")
  cat("\nRates:\n")
  cat(rate, "\n")
  if (length(bf) < 21) {
    cat("\nBase frequencies:  \n")
    print(bf)
    cat("\nRate matrix:\n")
    print(Q)
  }
}


#' @export
logLik.pmlMix <- function(object, ...) {
  res <- object$logLik
  attr(res, "df") <- sum(object$df[, 1] * object$df[, 2])
  class(res) <- "logLik"
  res
}