# $Id$
# CakeSummary: Functions to calculate statistics used in the summary,
# and display the summary itself.

# Parts modified from package mkin
# Parts Tessella (Rob Nelson/Richard Smith/Tamar Christina) for Syngenta: Copyright (C) 2011  Syngenta
# Tessella Project Reference: 6245, 7247

#    This program is free software: you can redistribute it and/or modify
#    it under the terms of the GNU General Public License as published by
#    the Free Software Foundation, either version 3 of the License, or
#    (at your option) any later version.
# 
#    This program is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.
# 
#    You should have received a copy of the GNU General Public License
#    along with this program.  If not, see <http://www.gnu.org/licenses/>.”

# Calculate the extra decay times for the other k values in DFOP
# and HS
# Arguments
#  type - type of compartment
#  parms.all - list of parameters
CakeExtraDT<-function(type, parms.all) {  
    DT50k1 = NA    
    DT50k2 = NA    
    if (!is.na(parms.all["k1"]) && !is.na(parms.all["k2"])) {
      k1 = parms.all["k1"]
      k2 = parms.all["k2"]
      DT50k1 = log(2)/k1
      DT50k2 = log(2)/k2
    }
    ret<-c(DT50k1, DT50k2)
    names(ret)<-c("k1", "k2")
    ret
}

# Calculate the decay times for a compartment
# Arguments
#  type - type of compartment
#  obs_var - compartment name
#  parms.all - list of parameters
# sannMaxIter - the maximum amount of iterations to do for SANN
CakeDT<-function(type, obs_var, parms.all, sannMaxIter) {    
    if (type == "SFO") {
      # Changed to new parameterisation
      #k_names = grep(paste("k", obs_var, sep="_"), names(parms.all), value=TRUE)
      k_name = paste("k", obs_var, sep="_")
      k_tot = parms.all[k_name]
      DT50 = log(2)/k_tot
      DT90 = log(10)/k_tot
    }
    if (type == "FOMC") {
      alpha = parms.all["alpha"]
      beta = parms.all["beta"]
      DT50 = beta * (2^(1/alpha) - 1)
      DT90 = beta * (10^(1/alpha) - 1)
    }
    if (type == "DFOP") {
      k1 = parms.all["k1"]
      k2 = parms.all["k2"]
      g = parms.all["g"]
      f <- function(t, x) {
        fraction <- g * exp( - k1 * t) + (1 - g) * exp( - k2 * t)
        (fraction - (1 - x/100))^2
      }

      DTminBounds <- 0.001
      DTminInitial <- 1
      DT50.temp <- optim(DTminInitial, f, method="SANN", control=list(fnscale=0.05, maxit=sannMaxIter), x = 50, lower = DTminBounds)
      DT50.o = DT50.temp$par
      DT50.converged = DT50.temp$convergence == 0
      DT50 = ifelse(!DT50.converged, NA, DT50.o)
      DT90.temp <- optim(DTminInitial, f, method="SANN", control=list(fnscale=0.05, maxit=sannMaxIter), x = 90, lower = DTminBounds)
      DT90.o = DT90.temp$par
      DT90.converged = DT90.temp$convergence == 0
      DT90 = ifelse(!DT90.converged, NA, DT90.o)
    }
    if (type == "HS") {
      k1 = parms.all["k1"]
      k2 = parms.all["k2"]
      tb = parms.all["tb"]
      DTx <- function(x) {
        DTx.a <- (log(100/(100 - x)))/k1
        DTx.b <- tb + (log(100/(100 - x)) - k1 * tb)/k2
        if (DTx.a < tb) DTx <- DTx.a
        else DTx <- DTx.b
        return(DTx)
      }
      DT50 <- DTx(50)
      DT90 <- DTx(90)
    }
    if (type == "SFORB") {
      # FOCUS kinetics (2006), p. 60 f
      k_out_names = grep(paste("k", obs_var, "free", sep="_"), names(parms.all), value=TRUE)
      k_out_names = setdiff(k_out_names, paste("k", obs_var, "free", "bound", sep="_"))
      k_1output = sum(parms.all[k_out_names])
      k_12 = parms.all[paste("k", obs_var, "free", "bound", sep="_")]
      k_21 = parms.all[paste("k", obs_var, "bound", "free", sep="_")]

      sqrt_exp = sqrt(1/4 * (k_12 + k_21 + k_1output)^2 + k_12 * k_21 - (k_12 + k_1output) * k_21)
      b1 = 0.5 * (k_12 + k_21 + k_1output) + sqrt_exp
      b2 = 0.5 * (k_12 + k_21 + k_1output) - sqrt_exp

      SFORB_fraction = function(t) {
        ((k_12 + k_21 - b1)/(b2 - b1)) * exp(-b1 * t) +
        ((k_12 + k_21 - b2)/(b1 - b2)) * exp(-b2 * t)
      }
      f_50 <- function(t) (SFORB_fraction(t) - 0.5)^2
      DTmin <- 0.001
      DT50.temp <- optim(DTmin, f_50, method="SANN", control=list(fnscale=0.05, maxit=sannMaxIter), x = 50, lower = DTmin)
      DT50.o = DT50.temp$par
      DT50.converged = DT50.temp$convergence == 0
      if (!DT50.converged) DT50 = NA else DT50 = DT50.o
      f_90 <- function(t) (SFORB_fraction(t) - 0.1)^2
      DT90.temp <- optim(DTmin, f_90, method="SANN", control=list(fnscale=0.05, maxit=sannMaxIter), x = 90, lower = DTmin)
      DT90.o = DT90.temp$par
      DT90.converged = DT90.temp$convergence == 0
      if (!DT90.converged) DT90 = NA else DT90 = DT90.o
    }
    ret<-c(DT50, DT90)
    names(ret)<-c("DT50","DT90")
    ret
}

# Compute chi2 etc
# Arguments
#  observed - data.frame of observed data
#  predicted_long - fitted values etc
#  obs_vars - compartment names
#  parms.optim - list of fitted parameters
#  state,ini.optim - list of fitted initial values
#
CakeChi2<-function(mkinmod, observed, predicted_long, obs_vars, parms.optim, state.ini.optim, state.ini, parms.ini) {
  # Calculate chi2 error levels according to FOCUS (2006)
    
  if(getRversion() >= '2.14.0'){
    # You would usually call mkinfit to fit the data, however it seems that we've already fit the data
    # bundle <- mkinfit(mkinmod, observed, parms.ini = parms.optim, state.ini = state.ini) #, err='err') 
    # Somewhere else. Calling mkinfit may result in an error during fitting. So Instead we just create
    # the values that the new version of mkinerrmin expects. There is no class check so it's fine.
    bundle<-vector()
    bundle$predicted <- predicted_long
    bundle$observed <- observed
    bundle$obs_vars <- obs_vars
    bundle$par <- c(parms.optim, state.ini.optim)
    errmin.overall <- mkinerrmin(bundle)
    
    errmin.overall
  } else {
    means <- aggregate(value ~ time + name, data = observed, mean, na.rm=TRUE)
    errdata <- merge(means, predicted_long, by = c("time", "name"), suffixes = c("_mean", "_pred"))
    errdata <- errdata[order(errdata$time, errdata$name), ]
    errmin.overall <- mkinerrmin(errdata, length(parms.optim) + length(state.ini.optim))
    
    errmin <- data.frame(err.min = errmin.overall$err.min, 
      n.optim = errmin.overall$n.optim, df = errmin.overall$df)
    rownames(errmin) <- "All data"
    for (obs_var in obs_vars)
    {
      errdata.var <- subset(errdata, name == obs_var)
      n.k.optim <- length(grep(paste("k", obs_var, sep="_"), names(parms.optim)))
      n.initials.optim <- length(grep(paste(obs_var, ".*", "_0", sep=""), names(state.ini.optim)))
      n.optim <- n.k.optim + n.initials.optim
      if ("alpha" %in% names(parms.optim)) n.optim <- n.optim + 1
      if ("beta" %in% names(parms.optim)) n.optim <- n.optim + 1
      if ("k1" %in% names(parms.optim)) n.optim <- n.optim + 1
      if ("k2" %in% names(parms.optim)) n.optim <- n.optim + 1
      if ("g" %in% names(parms.optim)) n.optim <- n.optim + 1
      if ("tb" %in% names(parms.optim)) n.optim <- n.optim + 1
      errmin.tmp <- mkinerrmin(errdata.var, n.optim)
      errmin[obs_var, c("err.min", "n.optim", "df")] <- errmin.tmp
    }
    errmin
  }
}

# Compute additional statistics (r²/efficiency) of obs v pred for each compartment and the whole problem
CakeAdditionalStats<-function(obsvspred){
	agg<-aggregate(obsvspred[c('observed', 'err-var', 'predicted', 'residual')], list(name=obsvspred$variable), function(x){x}, simplify=FALSE)
	frames<-apply(agg, 1, as.data.frame);
	names(frames)<-agg$name;
	frames$all<-obsvspred
	
	t(sapply(frames, function(frame){
		# This function takes a data frame for a single variable and makes the stats for it
		# r²: FOCUS eq 6.5 p. 97
		# Efficiency: eq 6.6 p. 99
		do <- frame$observed - mean(frame$observed)
		dp <- frame$predicted - mean(frame$predicted)
		r2 <- ( sum(do * dp) / sqrt(sum(do^2) * sum(dp^2)) ) ^ 2
		eff <- 1 - ( sum((frame$predicted - frame$observed)^2) / sum(do^2) )
		list(r2=r2, eff=eff)
	}))
}

# Summarise a fit - used for CakeIrlsFit and CakeOlsFit
summary.CakeFit <- function(object, data = TRUE, distimes = TRUE, halflives = TRUE, ff = TRUE, cov = FALSE,...) {
  param  <- object$par
  pnames <- names(param)
  p      <- length(param)
  covar  <- try(solve(0.5*object$hessian), silent = TRUE)   # unscaled covariance
  # covar  <- try(ginv(0.5*object$hessian))   # unscaled covariance, calculate using generic inversion

  rdf    <- object$df.residual
  resvar <- object$ssr / rdf
  modVariance <- object$ssr / length(object$residuals)
    
  # if(!is.numeric(covar)){
   # covar  <- try(ginv(0.5*object$hessian))
  # }
  
  if (!is.numeric(covar)) {
#    message <- "Cannot estimate covariance; system is singular"
#    warning(message)
#    covar <- matrix(data = NA, nrow = p, ncol = p)
   covar=NULL
  } else {
    message <- "ok"
    rownames(covar) <- colnames(covar) <-pnames
    se     <- sqrt(diag(covar) * resvar)
    names(se) <- pnames
    tval      <- param / se
  }

  if (!all(object$start$lower >=0)) {
    message <- "Note that the one-sided t-test may not be appropriate if
      parameter values below zero are possible."
    warning(message)
  } else message <- "ok"

  if(cov && !is.null(covar)) { 

    # Filter the values for t-test, only apply t-test to k-values  
    t.names  <- grep("k(\\d+)|k_(.*)", names(tval), value = TRUE)
    t.rest   <- setdiff(names(tval), t.names)
    t.values <- c(tval)
    t.values[t.rest] <- NA
    t.result <- pt(t.values, rdf, lower.tail = FALSE)
    
    # Now set the values we're not interested in for the lower 
    # and upper bound we're not interested in to NA
    t.param = c(param)
    t.param[t.names] <- NA
    # calculate the 90% confidence interval
    alpha <- 0.10
    lci90 <- t.param + qt(alpha/2,rdf)*se
    uci90 <- t.param + qt(1-alpha/2,rdf)*se
    
    # calculate the 95% confidence interval
    alpha <- 0.05
    lci95 <- t.param + qt(alpha/2,rdf)*se
    uci95 <- t.param + qt(1-alpha/2,rdf)*se

    param <- cbind(param, se, tval, t.result, lci90, uci90, lci95, uci95)
    dimnames(param) <- list(pnames, c("Estimate", "Std. Error",
                                    "t value", "Pr(>t)", "Lower CI (90%)", "Upper CI (90%)", "Lower CI (95%)", "Upper CI (95%)"))
                                    
    ans <- list(residuals = object$residuals,
                residualVariance = resvar,
                sigma = sqrt(resvar),
                modVariance = modVariance,
                df = c(p, rdf), cov.unscaled = covar,
                cov.scaled = covar * resvar,
                info = object$info, niter = object$iterations,
                stopmess = message,
                par = param)
  } else {
    param <- cbind(param)  
    ans <- list(residuals = object$residuals,
                residualVariance = resvar,
                sigma = sqrt(resvar),
                modVariance = modVariance,
                df = c(p, rdf),
                info = object$info, niter = object$iterations,
                stopmess = message,
                par = param)
    }

  ans$diffs <- object$diffs
  if(data) {
	ans$data <- object$data
	ans$additionalstats = CakeAdditionalStats(object$data)
  }
  ans$start <- object$start
  ans$fixed <- object$fixed
  ans$errmin <- object$errmin 
  ans$penalties <- object$penalties
  if(distimes) ans$distimes <- object$distimes
  if(halflives) ans$extraDT50 <- object$extraDT50
  if(ff) ans$ff <- object$ff
  if(length(object$SFORB) != 0) ans$SFORB <- object$SFORB
  class(ans) <- c("summary.CakeFit","summary.mkinfit", "summary.cakeModFit") 
  return(ans)  
}

# Print a summary. Used for CakeIrlsFit, CakeOlsFit and CakeMcmcFit
# Expanded from print.summary.cakeModFit
print.summary.CakeFit <- function(x, digits = max(3, getOption("digits") - 3), ...) {
  cat("\nEquations:\n")
  print(noquote(as.character(x[["diffs"]])))
  df  <- x$df
  rdf <- df[2]

  cat("\nStarting values for optimised parameters:\n")
  print(x$start)

  cat("\nFixed parameter values:\n")
  if(length(x$fixed$value) == 0) cat("None\n")
  else print(x$fixed)

  if ( !is.null(x$par) ) {
    cat("\nOptimised parameters:\n")
    printCoefmat(x$par, digits = digits, ...)
  }

  cat("\nResidual standard error:",
      format(signif(x$sigma, digits)), "on", rdf, "degrees of freedom\n")

  cat("\nChi2 error levels in percent:\n")
  x$errmin$err.min <- 100 * x$errmin$err.min
  print(x$errmin, digits=digits,...)

  printdistimes <- !is.null(x$distimes)
  if(printdistimes){
    cat("\nEstimated disappearance times:\n")
    print(x$distimes, digits=digits,...)
  }  
  
  printextraDT50 <- !is.null(x$extraDT50)
  if(printextraDT50){
    cat("\nHalf Lives for Extra k values:\n")
    print(x$extraDT50, digits=digits,...)
  }  

  printff <- !is.null(x$ff)
  if(printff){
    cat("\nEstimated formation fractions:\n")
    print(data.frame(ff = x$ff), digits=digits,...)
  }    

  printSFORB <- !is.null(x$SFORB)
  if(printSFORB){
    cat("\nEstimated Eigenvalues of SFORB model(s):\n")
    print(x$SFORB, digits=digits,...)
  }    

  printcor <- !is.null(x$cov.unscaled)
  if (printcor){
    Corr <- cov2cor(x$cov.unscaled)
    rownames(Corr) <- colnames(Corr) <- rownames(x$par)
    cat("\nParameter correlation:\n")
    print(Corr, digits = digits, ...)
  }

  printdata <- !is.null(x$data)
  if (printdata){
    cat("\nData:\n")
    print(format(x$data, digits = digits, scientific = FALSE,...), row.names = FALSE)
  }
  
  if(!is.null(x$additionalstats)){
	cat("\nAdditional Stats:\n");
	print(x$additionalstats, digits=digits, ...)
  }
  
  if(!(is.null(x$penalties) || 0 == dim(x$penalties)[[1]])){
	cat("\nPenalties:\n");
	print(x$penalties, digits=digits, row.names = FALSE, ...)
  }
  
  if ( !is.null(x$seed) ) {
      cat("\nRandom Seed:", x$seed, "\n")
  }
  invisible(x)
}