# an illustration of the rsm package for response surface experimentation

# -----------------------------------------------------------------------
# original sample of 8 points
# -----------------------------------------------------------------------

data <- scan(what = list(v1=0,v2=0,y=0), multi.line=F)
 180  180  158 
 220  180  168 
 180  220  176  
 220  220  182 
 200  200  175 
 200  200  174 
 200  200  171 
 200  200  173

data

rsmex  <- data.frame(data)
rm(data)

library(rsm)

coded.rsmex  <- coded.data(rsmex, x1 ~ (v1-200)/20, x2 ~ (v2-200)/20)

 # fit first-order model

rsmex.fo1 <- rsm(y ~ FO(x1, x2), data=coded.rsmex)

summary(rsmex.fo1)

# -----------------------------------------------------------------------
# a second sample of 8 points after following the method of steepest ascent
# -----------------------------------------------------------------------

data <- scan(what = list(v1=0,v2=0,y=0), multi.line=F)
 200  220  179  
 240  220  184 
 200  260  190 
 240  260  184 
 220  240  192 
 220  240  189 
 220  240  190 
 220  240  188

data

rsmex1  <- data.frame(data)
rm(data)

coded.rsmex1  <- coded.data(rsmex1, x1 ~ (v1-220)/20, x2 ~ (v2-240)/20)

 # fit first-order model

rsmex1.fo2 <- rsm(y ~ FO(x1, x2), data=coded.rsmex1)

summary(rsmex1.fo2)
 
# -----------------------------------------------------------------------
# final sample of 13 points for a CCD
# -----------------------------------------------------------------------

data <- scan(what = list(v1=0,v2=0,y=0), multi.line=F)
 200  220  179  
 240  220  184 
 200  260  190 
 240  260  184 
 248  240  184 
 192  240  185 
 220  268  190
 220  212  179
 220  240  192 
 220  240  189 
 220  240  190 
 220  240  188
 220  240  188

data

rsmex2  <- data.frame(data)
rm(data)

coded.rsmex2  <- coded.data(rsmex2, x1 ~ (v1-220)/20, x2 ~ (v2-240)/20)

rsmex2.so1  <- rsm(y ~ SO(x1, x2), data=coded.rsmex2)
summary(rsmex2.so1)

contour(rsmex2.so1, ~ x1 + x2, image=TRUE)