Nothing
#'@title Toth Isotherm Nonlinear Analysis
#'@name tothanalysis
#'@description Another empirical modification of the Langmuir equation with the
#'aim of reducing the error between experimental data and predicted value of
#'equilibrium data.
#'@param Ce the numerical value for the equilibrium capacity
#'@param Qe the numerical value for the fractional coverage
#'@import nls2
#'@import Metrics
#'@import stats
#'@import ggplot2
#'@return the nonlinear regression, parameters for Toth isotherm, and
#'model error analysis
#'@examples Ce <- c(0.01353, 0.04648, 0.13239, 0.27714, 0.41600, 0.63607, 0.80435, 1.10327, 1.58223)
#'@examples Qe <- c(0.03409, 0.06025, 0.10622, 0.12842, 0.15299, 0.15379, 0.15735, 0.15735, 0.16607)
#'@examples tothanalysis(Ce,Qe)
#'@author Keith T. Ostan
#'@author Chester C. Deocaris
#'@references Toth, J. (1971). State equations of the solid gas interface layer.
#'Acta Chem. Acad. Hung. 69:311-317
#'@export
# Building the Toth isotherm nonlinear form
tothanalysis <- function(Ce, Qe){
x <- Ce
y <- Qe
data <- data.frame(x,y)
# Toth isotherm nonlinear equation
fit1 <- y ~ (x)/(At+x)^(1/Nt) ##Kt is conditionally linear
# Setting of starting values
start1 <- data.frame(At = c(1, 100), Nt = c(0, 1))
# Fitting of the Toth isotherm via nls2
fit2 <- nls2::nls2(fit1, start = start1, data=data,
control = nls.control(maxiter = 100, warnOnly = TRUE),
algorithm = "plinear-random")
print("Toth Isotherm Nonlinear Analysis")
print(summary(fit2))
AIC <- AIC(fit2)
print("Aikake Information Criterion")
print(AIC(fit2))
print("Bayesian Information Criterion")
print(BIC(fit2))
# Error analysis of the Sips isotherm model
errors <- function (y) {
rmse <- Metrics::rmse(y, predict(fit2))
mae <- Metrics::mae(y, predict(fit2))
mse <- Metrics::mse(y, predict(fit2))
rae <- Metrics::rae(y, predict(fit2))
N <- nrow(na.omit(data))
SE <- sqrt((sum(y-predict(fit2))^2)/(N-2))
colnames(y) <- rownames(y) <- colnames(y)
list("Root Mean Squared Error" = rmse,
"Mean Absolute Error" = mae,
"Mean Squared Error" = mse,
"Relative Absolute Error" = rae,
"Standard Error for the Regression S" = SE)
}
a <- errors(y)
print(a)
rsqq <- lm(Qe~predict(fit2))
print(summary(rsqq))
# Graphical representation of the Toth isotherm model
### Predicted parameter values
parstoth <- as.vector(coefficients(fit2))
pars_At <- parstoth[1L];
pars_Nt <- parstoth[2L];
pars_Kt <- parstoth[3L]
rhs <- function(x){((pars_Kt*(x))/(pars_At+x)^(1/pars_Nt))}
#### Plot details
ggplot2::theme_set(ggplot2::theme_bw(10))
ggplot2::ggplot(data, ggplot2::aes(x = x, y = y)) + ggplot2::geom_point(color ="#3498DB" ) +
ggplot2::geom_function(color = "#D35400", fun = rhs ) +
ggplot2::labs(x = "Ce",
y = "Qe",
title = "Toth Isotherm Nonlinear Model",
caption = "PUPAIM") +
ggplot2::theme(plot.title=ggplot2::element_text(hjust = 0.5))
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.