[Rd] Make factanal accept functions for rotation parameter

[Haan, Stefan]

Dear Martin,

The thing I was trying to do, when I tried to pass a function for the
rotation parameter was to call factanal repeatedly with different
rotations to see which factor model would give the best
interpretability.

```R
rotate <- function(phi) {
	G <- matrix(c(cos(phi), sin(phi), -sin(phi), cos(phi)),
nrow=2, ncol=2)
	function(loadings) loadings %*% G
}

phi <- seq(0, pi/2, length.out=10)

par(mfcol=c(2,5))
for (i in 1:10) {
	model <- factanal(x=mydata, factors=2,
rotation=rotate(phi[i]), scores="regression")
	plot(model$scores[,1], model$scores[,2], type="n",
xlab="Factor 1", ylab="Factor 2", sub=paste("phi #",i,sep=""))
	text(model$scores[,1], model$scores[,2],
labels=rownames(mydata))
}
```

However thinking about it, I don't really want this to be an example in
the documentation as it quite wastefully recomputes the estimates for
the loadings and scores for each phi, when I could just fit the model
once and then multiply the loadings and scores with G(phi) and
t(G(phi)) respectively for each phi before plotting them.

Also, as Duncan Murdoch helpfully pointed out, the condition should
really be
```
is.function(rotation) || rotation != "none"
```
as != would fail before is.function(rotation) is evaluated.

Best greetings,
Stefan

On Thu, 2024-08-22 at 18:09 +0200, Martin Maechler wrote:
> > > > > > Haan, Stefan via R-devel 
> > > > > >     on Thu, 22 Aug 2024 14:03:09 +0000 writes:
> 
>     > Dear R developers,
>     > Would it be possible to make `factanal` to also accept
> functions and
>     > not just function names for its `rotation` parameter? If I
> understand
>     > correctly, `do.call` also supports this.
> 
>     > Best greetings,
>     > Stefan
> 
> > Index: src/library/stats/R/factanal.R
> > ===================================================================
> > --- src/library/stats/R/factanal.R	(revision 87038)
> > +++ src/library/stats/R/factanal.R	(working copy)
> > @@ -137,7 +137,7 @@
> >                        "unable to optimize from these starting
> > values"),
> >               domain = NA)
> >      load <- fit$loadings
> > -    if(rotation != "none") {
> > +    if(rotation != "none" || is.function(rotation)) {
> >          rot <- do.call(rotation, c(list(load), cn$rotate))
> >          load <- if (is.list(rot)) {
> >            load <- rot$loadings
> 
> I'm not a factanal user myself, but I think this is a very good,
> even "obvious" (in hindsight)  suggestion.
> .... unless I'm forgetting something.
> 
> Can you please provide useful (but *small*) example,  which I
> then also could add to the help page ?
> 
> Best regards,
> Martin
> 
> --
> Martin Maechler
> ETH Zurich  and   R Core team
>