# R/SSLorentz.R In OnofriAndreaPG/aomisc: Statistical methods for the agricultural sciences

#### Defines functions lorentz.4.initDRC.lorentz.4lorentz.4.funlorentz.3.initDRC.lorentz.3lorentz.3.fun

```# Bragg's equation
lorentz.3.fun <- function(X, b, d, e){
d / ( 1 + b * (X - e)^2)
}

DRC.lorentz.3 <- function(){
fct <- function(x, parm) {
lorentz.3.fun(x, parm[,1], parm[,2], parm[,3])
}
ssfct <- function(data){
# Get the data
x <- data[, 1]
y <- data[, 2]

d <- max(y)
e <- x[which.max(y)]

## Linear regression on pseudo-y and pseudo-x
pseudoY <- ( d - y )/ y
pseudoX <- (x - e)^2
coefs <- coef( lm(pseudoY ~ pseudoX - 1) )
b <- coefs[1]
start <- c(b, d, e)
return( start )
}
names <- c("b", "d", "e")
text <- "Lorentz equation with three parameters"

## Returning the function with self starter and names
returnList <- list(fct = fct, ssfct = ssfct, names = names, text = text)
class(returnList) <- "drcMean"
invisible(returnList)
}

lorentz.3.init <- function(mCall, LHS, data, ...) {
xy <- sortedXyData(mCall[["X"]], LHS, data)
x <-  xy[, "x"]; y <- xy[, "y"]

d <- max(y)
e <- x[which.max(y)]

## Linear regression on pseudo-y and pseudo-x
pseudoY <- ( d - y )/ y
pseudoX <- (x - e)^2
coefs <- coef( lm(pseudoY ~ pseudoX - 1) )
b <- coefs[1]
start <- c(b, d, e)
names(start) <- mCall[c("b", "d", "e")]
start
}

NLS.lorentz.3 <- selfStart(lorentz.3.fun, lorentz.3.init, parameters=c("b", "d", "e"))

lorentz.4.fun <- function(X, b, c, d, e){
c + (d - c) / ( 1 + b * (X - e)^2)
}

DRC.lorentz.4 <- function(){
fct <- function(x, parm) {
lorentz.4.fun(x, parm[,1], parm[,2], parm[,3], parm[,4])
}
ssfct <- function(data){
# Get the data
x <- data[, 1]
y <- data[, 2]

d <- max(y)
c <- min(y) * 0.95
e <- x[which.max(y)]

## Linear regression on pseudo-y and pseudo-x
pseudoY <- (d - y)/(y - c)
pseudoX <- (x - e)^2
coefs <- coef( lm(pseudoY ~ pseudoX - 1) )
b <- coefs[1]
start <- c(b, c, d, e)
return( start )
}
names <- c("b", "c", "d", "e")
text <- "Lorentz equation with four parameters"

## Returning the function with self starter and names
returnList <- list(fct = fct, ssfct = ssfct, names = names, text = text)
class(returnList) <- "drcMean"
invisible(returnList)
}

lorentz.4.init <- function(mCall, LHS, data, ...) {
xy <- sortedXyData(mCall[["X"]], LHS, data)
x <-  xy[, "x"]; y <- xy[, "y"]

d <- max(y)
c <- min(y) * 0.95
e <- x[which.max(y)]

## Linear regression on pseudo-y and pseudo-x
pseudoY <- (d - y)/(y - c)
pseudoX <- (x - e)^2
coefs <- coef( lm(pseudoY ~ pseudoX - 1) )
b <- coefs[1]
start <- c(b, c, d, e)
names(start) <- mCall[c("b", "c", "d", "e")]
start
}

NLS.lorentz.4 <- selfStart(lorentz.4.fun, lorentz.4.init, parameters=c("b", "c", "d", "e"))
```
OnofriAndreaPG/aomisc documentation built on Feb. 26, 2024, 8:21 p.m.