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##==============================================================================
## Function to calibrate vital rates to match the desired lambda ==
##==============================================================================
#' Calibration of vital rate values
#' Function to adjust the vital rates values in order to match the desired population growth rate
#'
#' @param inits intial values of survival and fecundities for the optimization
#' @param f a vector of survival probabilities for each age class
#' @param s a vector of fecundity values for each age clas
#' @param lam0 the desired population growth rate - the one to be matched
#'
#' @return a vector of adjusted values of survival and fecundities
#' @export
#'
#' @import popbio
#' @import magrittr
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#' @rawNamespace import(stats, except = c(filter, lag))
#'
#' @examples
#' s <- c(0.5, 0.7, 0.8, 0.95)
#' f <- c(0, 0, 0.05, 0.55)
#' calibrate_params(inits = NULL, s = s, f = f, lam0 = 1.08)
#'
calibrate_params <- function(inits = NULL, s, f, lam0){
nac <- length(s)
lam00 <- build_Leslie(s, f) %>% lambda
fu <- f[f != 0]
fo <- f[f == 0]
## Utility function to optimize
uti_fun <- function(pars, fo, nac, lam0){
s <- tail(pars, nac)
fu <- head(pars, -nac)
lam00 <- build_Leslie(s, f=c(fo, fu)) %>% lambda
return(abs(lam0-lam00))
}
# End utility function
# Set parameter boundaries for the optimization
if(lam0 - lam00 < 0){
lower = c(rep(0, length(fu)), apply(cbind((s*0.5), 0.05), 1, max))
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upper = c(fu, s)*1.01
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lower = c(fu, s)*0.99
upper = c(rep(10, length(fu)), apply(cbind((s*1.25), 0.98), 1, min))
}
# Set initial values
if(is.null(inits)) inits <- c(fu, s)
# Optimize the utility function
opt <- stats::optim(par = inits, fn = uti_fun, fo=fo, nac=nac, lam0=lam0,
lower = lower, upper = upper, method="L-BFGS-B")
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# Return output : New fecundity vector
params <- c(tail(opt$par, nac), fo, head(opt$par, -nac))
names(params) <- c(paste0("s", 1:nac), paste0("f", 1:nac))
return(params)
} # End function
################################################################################
##==============================================================================
## Function to choose initial values for the calibration of vital rates ==
##==============================================================================
#' Set initial values for the calibration of vital rates.
#' This function can be used to speed up the optim process of the 'calibrate_params' function.
#'
#' @param s a vector of survival probabilities for each age class
#' @param f a vector of fecundity values for each age clas
#' @param lam0 the desired population growth rate - the one to be matched
#'
#' @return a vetor of initial values for the calibration of survival and fecundity values
#' @export
#'
#' @examples
#' s <- c(0.5, 0.7, 0.8, 0.95)
#' f <- c(0, 0, 0.05, 0.55)
#' init_calib(s = s, f = f, lam0 = 1.08)
#'
init_calib <- function(s, f, lam0){
A00 <- build_Leslie(s=s, f=f)
diff_rel_lam <- (lam0 - lambda(A00))/lambda(A00)
d <- match_lam_delta(diff_rel_lam = diff_rel_lam, s=s, f=f)
nac = length(s)
inits_vr <- c(s,f) + d
inits_vr <- c(tail(inits_vr, nac), head(inits_vr, nac) %>% sapply(min, 0.999))
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inits <- inits_vr[inits_vr != 0]
return(inits)
} # End function
################################################################################
##==============================================================================
## Function to infer the difference to apply to vital rates ==
##==============================================================================
#' Function to calculate the difference to apply to each vital rates to match the desired
#' population growth rate (lambda).
#' This function is used in the 'init_calib' function.
#'
#' @param diff_rel_lam a number. The relative difference of lambda (population growth rate)
#' to be matched
#' @param s a vector of survival probabilities for each age class
#' @param f a vector of fecundity values for each age clas
#'
#' @return a vector of (absolute) difference to apply
#' @export
#'
#' @examples
#' s <- c(0.5, 0.7, 0.8, 0.95)
#' f <- c(0, 0, 0.05, 0.55)
#'
#' # Match for a 5% decrease in lambda
#' match_lam_delta(diff_rel_lam = -0.05, s, f)
match_lam_delta <- function(diff_rel_lam, s, f){
nac = length(s)
vr = c(s, f)
A00 <- build_Leslie(s=s, f=f)
# Infer the DELTA for each vital rate
d <- diff_rel_lam*vr/(lambda(A00))
names(d) <- c(paste0("s", 1:nac), paste0("f", 1:nac))
return(d)
} # End function
################################################################################