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#' Equation 12
#'
#' @description Equation in Montagnes et al (2008) citing Flinn (1991)
#'
#' @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 depends on augment: if false, fitting parameters or fitted data
#' @export
#'
#' @examples output <- with(Emiliania_huxleyi, equ12(temp=temp, rate=rate))
equ12 <- function(temp,rate,augment=F, return_fit=F){
#Fit the function
try_test <- try({
c=0.005
b=(-2*c*temp[rate==max(rate)])[1]
a= -min(b*temp +c*(temp^2))
fit = minpack.lm::nlsLM(rate ~ 1/(1+a + b*temp +c*(temp^2)),
control = minpack.lm::nls.lm.control(maxiter = 10^20),start = list(a=a, b=b,c=1))
output <- broom::tidy(fit)
a <- output$estimate[output$term=="a"]
b <- output$estimate[output$term=="b"]
c <- output$estimate[output$term=="c"]
f_equ= function(t){1/(1+ a + b*t + c *t^2)} #for use with optimise
})
output <- temperatureresponse::amend_output(output,
fit,
f_equ,
temp,
rate,
try_test,
augment,
return_fit)
output$model <- "equ12"
print("equ12")
return(output)
}
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