R Under development (unstable) (2023-10-08 r85282 ucrt) -- "Unsuffered Consequences"
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> # Any necessary setup
> library(rpart)
> options(na.action="na.omit")
> options(digits=4) # to match earlier output
> set.seed(1234)
> 
> mystate <- data.frame(state.x77, region=factor(state.region))
> names(mystate) <- c("population","income" , "illiteracy","life" ,
+        "murder", "hs.grad", "frost",     "area",      "region")
> #
> # Test out the "user mode" functions, with an anova variant
> #
> 
> # The 'evaluation' function.  Called once per node.
> #  Produce a label (1 or more elements long) for labeling each node,
> #  and a deviance.  The latter is
> #	- of length 1
> #       - equal to 0 if the node is "pure" in some sense (unsplittable)
> #       - does not need to be a deviance: any measure that gets larger
> #            as the node is less acceptable is fine.
> #       - the measure underlies cost-complexity pruning, however
> temp1 <- function(y, wt, parms) {
+     wmean <- sum(y*wt)/sum(wt)
+     rss <- sum(wt*(y-wmean)^2)
+     list(label= wmean, deviance=rss)
+     }
> 
> # The split function, where most of the work occurs.
> #   Called once per split variable per node.
> # If continuous=T
> #   The actual x variable is ordered
> #   y is supplied in the sort order of x, with no missings,
> #   return two vectors of length (n-1):
> #      goodness = goodness of the split, larger numbers are better.
> #                 0 = couldn't find any worthwhile split
> #        the ith value of goodness evaluates splitting obs 1:i vs (i+1):n
> #      direction= -1 = send "y< cutpoint" to the left side of the tree
> #                  1 = send "y< cutpoint" to the right
> #         this is not a big deal, but making larger "mean y's" move towards
> #         the right of the tree, as we do here, seems to make it easier to
> #         read
> # If continuos=F, x is a set of integers defining the groups for an
> #   unordered predictor.  In this case:
> #       direction = a vector of length m= "# groups".  It asserts that the
> #           best split can be found by lining the groups up in this order
> #           and going from left to right, so that only m-1 splits need to
> #           be evaluated rather than 2^(m-1)
> #       goodness = m-1 values, as before.
> #
> # The reason for returning a vector of goodness is that the C routine
> #   enforces the "minbucket" constraint. It selects the best return value
> #   that is not too close to an edge.
> temp2 <- function(y, wt, x, parms, continuous) {
+     # Center y
+     n <- length(y)
+     y <- y- sum(y*wt)/sum(wt)
+ 
+     if (continuous) {
+ 	# continuous x variable
+ 	temp <- cumsum(y*wt)[-n]
+ 
+ 	left.wt  <- cumsum(wt)[-n]
+ 	right.wt <- sum(wt) - left.wt
+ 	lmean <- temp/left.wt
+ 	rmean <- -temp/right.wt
+ 	goodness <- (left.wt*lmean^2 + right.wt*rmean^2)/sum(wt*y^2)
+ 	list(goodness= goodness, direction=sign(lmean))
+ 	}
+     else {
+ 	# Categorical X variable
+ 	ux <- sort(unique(x))
+ 	wtsum <- tapply(wt, x, sum)
+ 	ysum  <- tapply(y*wt, x, sum)
+ 	means <- ysum/wtsum
+ 
+ 	# For anova splits, we can order the categories by their means
+ 	#  then use the same code as for a non-categorical
+ 	ord <- order(means)
+ 	n <- length(ord)
+ 	temp <- cumsum(ysum[ord])[-n]
+ 	left.wt  <- cumsum(wtsum[ord])[-n]
+ 	right.wt <- sum(wt) - left.wt
+ 	lmean <- temp/left.wt
+ 	rmean <- -temp/right.wt
+ 	list(goodness= (left.wt*lmean^2 + right.wt*rmean^2)/sum(wt*y^2),
+ 	     direction = ux[ord])
+ 	}
+     }
> 
> # The init function:
> #   fix up y to deal with offsets
> #   return a dummy parms list
> #   numresp is the number of values produced by the eval routine's "label"
> #   numy is the number of columns for y
> #   summary is a function used to print one line in summary.rpart
> # In general, this function would also check for bad data, see rpart.poisson
> #   for instace.
> temp3 <- function(y, offset, parms, wt) {
+     if (!is.null(offset)) y <- y-offset
+     list(y=y, parms=0, numresp=1, numy=1,
+ 	      summary= function(yval, dev, wt, ylevel, digits ) {
+ 		  paste("  mean=", format(signif(yval, digits)),
+ 			", MSE=" , format(signif(dev/wt, digits)),
+ 			sep='')
+ 	     })
+     }
> 
> 
> alist <- list(eval=temp1, split=temp2, init=temp3)
> 
> fit1 <- rpart(income ~population +illiteracy  + murder + hs.grad + region,
+ 	     mystate, control=rpart.control(minsplit=10, xval=0),
+ 	     method=alist)
> 
> fit2 <- rpart(income ~population +illiteracy + murder + hs.grad + region,
+ 	     mystate, control=rpart.control(minsplit=10, xval=0),
+ 	      method='anova')
> 
> # Other than their call statement, and a longer "functions" component in
> #  fit1, fit1 and fit2 should be identical.
> all.equal(fit1$frame, fit2$frame)
[1] TRUE
> all.equal(fit1$splits, fit2$splits)
[1] TRUE
> all.equal(fit1$csplit, fit2$csplit)
[1] TRUE
> all.equal(fit1$where, fit2$where)
[1] TRUE
> all.equal(fit1$cptable, fit2$cptable)
[1] TRUE
> 
> # Now try xpred on it
> xvtemp <- rep(1:5, length=50)
> xp1 <- xpred.rpart(fit1, xval=xvtemp)
> xp2 <- xpred.rpart(fit2, xval=xvtemp)
> aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))
> aeq(xp1, xp2)
[1] TRUE
> 
> fit3 <- rpart(income ~population +illiteracy + murder + hs.grad + region,
+ 	     mystate, control=rpart.control(minsplit=10, xval=xvtemp),
+ 	      method='anova')
> zz <- apply((mystate$income - xp1)^2,2, sum)
> aeq(zz/fit1$frame$dev[1], fit3$cptable[,4])  #reproduce xerror
[1] TRUE
> 
> zz2 <- sweep((mystate$income-xp1)^2,2, zz/nrow(xp1))
> zz2 <- sqrt(apply(zz2^2, 2, sum))/ fit1$frame$dev[1]
> aeq(zz2, fit3$cptable[,5])          #reproduce se(xerror)
[1] TRUE
> 
> 
> proc.time()
   user  system elapsed 
   0.28    0.01    0.29