# Import minpac.lm for Levenberg-Marquardt algorithm
library(minpack.lm)

# Open dialog to select text data file
data <- read.table(file.choose())

# Separate the data into f, zr, and zi
f <- data[,1,1]
zr <- data[,2,1]
zi <- data[,3,1]

zz <- c(zr, zi)

# Complex impedance data list
zc <- zr + 1i*zi

# Declare impedance model function
imp <- function(p,x){
  z <- p[1]
  z <- z + p[2]/(1+p[2]*p[3]*(1i*2*pi*x)^p[4])
  z <- z + p[5]/(1+p[5]*p[6]*(1i*2*pi*x)^p[7])
  z <- z + p[8]/(1+p[8]*p[9]*(1i*2*pi*x)^p[10])
  return(z)
}

# Declare the residual function
rsd <- function(p,z,x) {
  errz = imp(p,x)-z
  err = c(Re(errz), Im(errz))
  return (err)
}

# Input an initial guess of the fitting parameters
p0 <- c(11, 5, 5.0e-5, 0.6, 3, 1.0e-4, 0.7, 4, 1.0e-3, 0.85)
# Lower limit of parameters
pl <- c(0.1, 0.1, 1e-10, 0.4, 0.1, 1e-10, 0.4, 0.1, 1e-10, 0.4)

# Upper limit of parameters
pu <- c(50, 50, 1e-2, 1, 50, 1e-2, 1, 50, 1e-1,1)


# start fitting
nls.out <- nls.lm(p = p0, lower = pl, upper = pu, fn = rsd, z = zz, x = f, control = nls.lm.control(nprint = 1, maxfev = 3000, maxiter = 500, ftol = 1.0e-30))

summary(nls.out)
aa <- summary(nls.out)

pfit <- coef(nls.out)
perr <- aa[[8]][11:20]
fcov <- vcov(nls.out)
RSS <- sum(abs(imp(pfit,f)-zc)*abs(imp(pfit,f)-zc))

while (aa[[5]] != 1){
	p0 <- pfit
	nls.out <- nls.lm(p = p0, lower = pl, upper = pu, fn = rsd, z = zc, x = f, control = nls.lm.control(nprint = 1, maxfev = 3000, maxiter = 500, ftol = 0.00001))
	summary(nls.out)
	aa <- summary(nls.out)
	}

summary(nls.out)
aa <- summary(nls.out)
pfit <- coef(nls.out)
perr <- aa[[8]][11:20]
RSS <- sum(abs(imp(pfit,f)-zc)*abs(imp(pfit,f)-zc))



zc_cal <- imp(pfit,f)
zr_cal <- Re(zc_cal)
zi_cal <- Im(zc_cal)

plot(f,zr,log="x", xlim=c(10^-2, 10^6),ylim=c(10, 25),ann=F)
par(new=T)
plot(f,zr_cal,log="x", xlim=c(10^-2, 10^6),ylim=c(10, 25), type="l")

dev.new()
plot(f,zi,log="x", xlim=c(10^-2, 10^6),ylim=c(-2.5, 0.5),ann=F)
par(new=T)
plot(f,zi_cal,log="x", xlim=c(10^-2, 10^6),ylim=c(-2.5, 0.5),type="l")

dev.new()
plot(zr,-zi,xlim=c(10,25),ylim=c(-2, 5),ann=F, asp = 1)
par(new=T)
plot(zr_cal,-zi_cal, xlim=c(10,25),ylim=c(-2, 5), type="l", asp = 1)

pfit
perr
RSS