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#' Equation 4
#'
#' @description Equation 4 is model H in Li & Dickie (1987) citing Hinshelwood (1947)
#'
#' @param temp temperature (in Celsius)
#' @param rate rate measurement
#' @param augment logical wether the dataset with fits should be returned instead of the parameter values
#' @param return_fit logical wether the model fit object should be returned
#'
#' @return a data frame of, depending on augment argument, if FALSE, parameters, if TRUE, data with predicted values
#' @export
#'
#' @examples output <- with(Emiliania_huxleyi, equ4(temp=temp, rate=rate))
equ4 <- function(temp,rate, augment=F, return_fit=F){
#Fit the function
try_test <- try({
R<-0.001987
fit = minpack.lm::nlsLM(rate ~ a*exp(-b/(R*(temp+273.15)))-c*exp(-d/(R*(temp+273.15))),
start = list(a=1.43e10, b=12.3,c=2.13e16,d=21),
control = minpack.lm::nls.lm.control(maxiter = 10^20))
output <- broom::tidy(fit)
a <- output$estimate[output$term=="a"]
b <- output$estimate[output$term=="b"]
c <- output$estimate[output$term=="c"]
d <- output$estimate[output$term=="d"]
f_equ= function(t){a*exp(-b/(R*t))-c*exp(-d/(R*t))} #- for use with optim
})
output <- temperatureresponse::amend_output(output,
fit,
f_equ,
temp,
rate,
try_test,
augment,
return_fit)
output$model <- "equ04"
print("equ04")
return(output)
}
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