### Filename: plotMathProblem.R
### Paul Johnson July 7, 2010
### email me <pauljohn@ku.edu>

### This is a tale of "coercion" of items in vectors.

### Run this code through and see if you can explain the
### puzzle at the end.

sigma <- 10.0
mu <- 4.0

myx <- seq( mu - 3.5*sigma,  mu+ 3.5*sigma, length.out=500)

myDensity <- dnorm(myx,mean=mu,sd=sigma)

### xpd needed to allow writing outside strict box of graph
### Need big bottom margin to add several x axes
par(xpd=TRUE, ps=10, mar=c(18,2,2,2))

plot(myx, myDensity, type="l", xlab="", ylab="Probability Density ", main="Normal", axes=FALSE)
axis(2, pos= mu - 3.6*sigma)
axis(1, pos=0)

lines(c(myx,myx[length(myx)]),c(0,0)) ### closes off axes

for (i in 1:(length(x))){
lines( c(x[i],x[i]), c(0, dnorm(x[i],m=m,sd=sd)), lty= 14, lwd=.2)
}
}

dividers <- c(qnorm(0.025), -1, 0, 1, qnorm(0.975))

# bquote gets the value of mu from the environment with .(mu).
t1 <- bquote( mu == .(mu))
mtext(t1, 1, at=mu, line=-1)

addInteriorLabel <- function(pos1, pos2, m, s){
area <- abs(100*( pnorm(m+pos1*s,m,s)-pnorm(m+pos2*s, m,s)))
mid <- m+0.5*(pos1+pos2)*s
text(mid, 0.5*dnorm(mid,m,s),label=paste(round(area,2),"%"))
}

b1 <- substitute( mu ~ d*sigma, list(d=round(dividers,2)))
b2 <- substitute( mu ~ d*sigma, list(d=round(dividers,2)))
b3 <- substitute( mu )
b4 <- substitute( mu + d*sigma, list(d=round(dividers,2)))
b5 <- substitute( mu + d*sigma, list(d=round(dividers,2)) )

## 1. Fails, labels not ready yet. R needs expressions to do plotmath

## 2. Also fails, but in an interesting way. Puzzle. Why do all
## but b1 display properly.

## 3. Works, probably the recommended way
### Duncan Murdoch explained that as.expression is needed in r-help.
### The reason that "as." is required is difficult, I think.

## 4. Also Works, but hard to understand why. ##  Why does it work with the as.expression applied only to first
## element?

### Puzzle: Why does 2 fail, and why does 4 work?

### Several r-help members helped me understand this.
### It comes back to this:
### a vector in R has to be a homogeneous collection of items.
### All elements have to be numbers, or characters, or expressions.

### Putting things into a vector with c() signals R
### you want to "coerce" all of the things into the same type.
### What happens if you do
### x <- c("a", 1, 2, 3, 4) ##?
### You don't end up with one character and 4 numbers.  You get 5
### characters.
### > x
###  "a" "1" "2" "3" "4"
### Behind the scenes, R applies "as.character".

### Try #2 sets the first thing as expression(b1), and
### then in the effort to build the vector, R runs "as.expression"
### on b2, b3, b4, b5 automatically. Because "as.expression" is the
### required fix, then we get the correct output for those items.

### Why does Try #4 succeed?  Same answer.  After the first item
### is seen as an expression, then R coerces the rest with as.expression.

### So the approach in #4 works, but only luckily, and when #2 failed,
### it creates a very hard to debug problem (for me, at least).

### Anyway, now that this "works" I can concentrate on putting this to
### use in another project.