---
title: "MixOptim basic usage"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{basic}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

This vignette demonstrates the basic usage of MixOptim functions to perform a basic optimization and plot.

# Basic usage

The following code will perform a full range optimization of a mixture of 3 compounds based on two antagonist responses.


```{r setup}
library(MixOptim)
```

```{r}
saPred<-function(x) 17.3359 * x[1] + 30.7765 * x[2] + 20.0501 * x[3] + 0.7506 * x[1] * x[2] + (-6.3443 * x[1] * x[3]) + (-5.9291 * x[2] * x[3]) +(-25.3093 * x[1] * x[2] * x[3])
pvPred<-function(x)  0.884640 * x[1] + 0.789863 * x[2] + 0.825016 * x[3] + (-0.108964 * x[1] * x[2]) + 0.107167 * x[1] * x[3] + (-0.005220 * x[2] * x[3]) + 1.625246 * x[1] * x[2] * x[3]


funcoes <- c(saPred, pvPred) 
saD<-dMin(16.8293856, 31.41170555) # from experimental data
pvD<-dMax(0.7796004, 0.9019796) # from experimental data
overallD<-dOverall(saD, pvD)

a <- mixtureOptim(funcoes, overallD, 3, step = 0.01, plot = T)
desirabilityPlot(funcoes, a$plotData, a$bestComposition, list(saD, pvD), c("min", "max"))
```

If the user want to get a more accurate composition, it is possible to do an optimization within a specific range (points +- alpha) based on previous values:

```{r}
b <- mixtureFineOptim(funcoes, overallD, startPoint = a$bestComposition, step = 0.0001, alpha = 0.015)
b
desirabilityPlot(funcoes, a$plotData, b$bestComposition, list(saD, pvD), c("min", "max"))
```

# Restricting seach intervals

```{r}
# data
dados <- read.table(header = T, sep = "\t", text = "
ID	TiO2	Vehicle	Extender A	Extender B	Hiding	Scrub
1	0.05	0.20	0.30	0.45	7.8953	533.67
2	0.45	0.20	0.30	0.05	32.862	749
3	0.05	0.60	0.30	0.05	3.721	39.5
4	0.05	0.20	0.70	0.05	9.2751	203.25
5	0.25	0.20	0.30	0.25	20.132	555.25
6	0.05	0.40	0.30	0.25	4.7137	51.75
7	0.05	0.20	0.50	0.25	8.3829	342.75
8	0.25	0.40	0.30	0.05	16.245	84.75
9	0.25	0.20	0.50	0.05	22.639	360.75
10	0.05	0.40	0.50	0.05	5.4645	48
11	0.05	0.33	0.43	0.18	5.8882	76
12	0.18	0.20	0.43	0.18	17.256	386.25
13	0.18	0.33	0.30	0.18	12.351	136
14	0.18	0.33	0.43	0.05	14.499	75.5
15	0.10	0.25	0.35	0.30	10.548	325.75
16	0.30	0.25	0.35	0.10	22.096	359
17	0.10	0.45	0.35	0.10	6.2888	40.75
18	0.10	0.25	0.55	0.10	10.629	136.67
19	0.15	0.30	0.40	0.15	11.777	114")

# function with coefficients generated with lm()
hiding<-function(x) 67.748*x[1] + 7.291*x[2] + 11.419*x[3] + 14.578*x[4] - 64.32*x[1]*x[2] + 35.878*x[1]*x[3] - 15.696*x[1]*x[4] - 31.006*x[2]*x[3] - 38.668*x[2]*x[4] - 6.59*x[3]*x[4]
scrub<-function(x) 3937.5*x[1] + 899.3*x[2] + 502*x[3] + 2354.8*x[4] - 8227.2*x[1]*x[2] - 3227.4*x[1]*x[3] - 2447.7*x[1]*x[4] - 2435.3*x[2]*x[3] - 6325.1*x[2]*x[4] - 1050.3*x[3]*x[4]

funcoes2 <- c(hiding, scrub) 
des1<-dMax(min(dados$Hiding), max(dados$Hiding)) 
des2<-dMin(min(dados$Scrub), max(dados$Scrub))
finalD<-dOverall(des1, des2)

# optimize and generate data for plot
teste <- mixtureRangeOptim(funcoes2, finalD, midPoints = c(0.25, 0.4, 0.5, 0.25), alpha = c(0.2, 0.2, 0.2, 0.2), step = 0.01, plot=T)
# find a more accurate value based on previous composition, ingoring the last one and not generating plot data
teste2 <- mixtureRangeOptim(funcoes2, finalD, midPoints = teste$bestComposition, alpha = c(0.01, 0.01, 0.01, 0), step = 0.001, plot=F)
teste2

# plot result
desirabilityPlot(funcoes2, teste$plotData, teste2$bestComposition, list(des1, des2), c("max", "min"))
```

# More specific desirability models: full example

```{r}
# data
dados <- read.table(header = T, dec = ",", sep = "\t", text = "
x1	x2	x3	R1	R2	R3
1	0	0	0,76	8	5
1	0	0	0,75	8	5
0,5	0,5	0	1,4	7	7,5
0,5	0	0,5	0,55	8	10
0	1	0	4,1	4	10
0	1	0	4,4	4	10
0	0,5	0,5	0,9	7	12,5
0	0	1	0,42	9	15
0	0	1	0,4	10	15
0,6667	0,1667	0,1667	0,8	7	7,5
0,1667	0,6667	0,1667	1,7	7	10
0,1667	0,1667	0,6667	0,55	8	12,5
0,3333	0,3333	0,3333	0,8	8	10")

# create models, verify coefficients and significante, and generate functions
lm1 <- lm(data = dados, R1 ~ -1 + x1 + x2 + x3 + x1:x2 + x1:x3 + x2:x3)
summary(lm1)
flm1 <- function(x) 0.7678*x[1] + 4.2083*x[2] + 0.4274*x[3] - 4.3273*x[1]*x[2] + 0.3070*x[1]*x[3] - 5.6101*x[2]*x[3]
lm2 <- lm(data = dados, R2 ~ -1 + x1 + x2 + x3)
summary(lm2)
flm2 <- function(x) 7.9742*x[1] + 4.5742*x[2] + 9.3742*x[3]
lm3 <- lm(data = dados, R3 ~ -1 + x1 + x2 + x3)
summary(lm3)
flm3 <- function(x) 4.9998461*x[1] + 9.9998461*x[2] + 14.9998461*x[3]

funcoes2 <- c(flm1, flm2, flm3) 
# specific range and target for Y1
des1<-dTarget(0.5, 0.6, 0.7)
des2<-dMax(8, max(dados$R2))
des3<-dMin(5, 10)
finalD<-dOverall(des1, des2, des3)

# full range optimization
teste <- mixtureOptim(funcoes2, finalD, 3, step = 0.01, plot = T)
# plot
desirabilityPlot(funcoes2, teste$plotData, teste$bestComposition, list(des1, des2, des3), c("max", "max", "min"))

# more accurate optimization within +- 0.02 (default value for alpha)
teste2 <- mixtureFineOptim(funcoes2, finalD, teste$bestComposition, step = 0.0001)
teste2
# plot
desirabilityPlot(funcoes2, teste$plotData, teste2$bestComposition, list(des1, des2, des3), c("max", "max", "min"))
```
