R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("GPArotation-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('GPArotation')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "GPA"
> 
> ### * GPA
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: GPA
> ### Title: Rotation optimization
> ### Aliases: GPForth GPFoblq
> ### Keywords: multivariate
> 
> ### ** Examples
> 
>   data("Harman", package="GPArotation")
>   qHarman  <- GPForth(Harman8, Tmat=diag(2), method="quartimax")
> 
>   data("WansbeekMeijer", package="GPArotation")
>   fa.unrotated  <- factanal(factors = 2, covmat=NetherlandsTV, 
+               normalize=TRUE, rotation="none")
> 
>   GPForth(loadings(fa.unrotated), method="varimax", normalize=TRUE)$Lh
           Factor1    Factor2
NL1      0.2296980 -0.7570052
TV2      0.3254766 -0.7745330
NL3      0.2279537 -0.7388609
RTL4     0.6348515 -0.2998743
RTL5     0.7073135 -0.2782447
Veronica 0.7893605 -0.2141181
SBS6     0.6988858 -0.1990791
> 
>   TV <- GPFoblq(loadings(fa.unrotated), method="oblimin", normalize=TRUE)
> 
>   print(TV)
Oblique rotation method Oblimin Quartimin converged.
Loadings:
         Factor1 Factor2
NL1      -0.0245 -0.8055
TV2       0.0822 -0.7884
NL3      -0.0194 -0.7847
RTL4      0.6350 -0.1038
RTL5      0.7294 -0.0495
Veronica  0.8518  0.0589
SBS6      0.7504  0.0409

Rotating matrix:
      [,1]   [,2]
[1,] 0.562 -0.556
[2,] 1.115  1.118

Phi:
       [,1]   [,2]
[1,]  1.000 -0.599
[2,] -0.599  1.000
>   print(TV, Table=TRUE)
Oblique rotation method Oblimin Quartimin converged.
Loadings:
         Factor1 Factor2
NL1      -0.0245 -0.8055
TV2       0.0822 -0.7884
NL3      -0.0194 -0.7847
RTL4      0.6350 -0.1038
RTL5      0.7294 -0.0495
Veronica  0.8518  0.0589
SBS6      0.7504  0.0409

Rotating matrix:
      [,1]   [,2]
[1,] 0.562 -0.556
[2,] 1.115  1.118

Phi:
       [,1]   [,2]
[1,]  1.000 -0.599
[2,] -0.599  1.000

Iteration table:
      [,1]   [,2]     [,3]  [,4]
 [1,]    0 0.5335 -0.52594 1.000
 [2,]    1 0.5274 -0.95379 0.125
 [3,]    2 0.5239 -0.83755 0.250
 [4,]    3 0.5103 -0.63500 0.500
 [5,]    4 0.4332 -0.32908 1.000
 [6,]    5 0.2767 -0.00785 1.000
 [7,]    6 0.1404 -0.23170 0.250
 [8,]    7 0.0539 -0.33988 0.500
 [9,]    8 0.0214 -1.05883 0.250
[10,]    9 0.0206 -1.36695 0.125
[11,]   10 0.0205 -1.69920 0.125
[12,]   11 0.0204 -2.04440 0.125
[13,]   12 0.0204 -2.39584 0.125
[14,]   13 0.0204 -2.75016 0.125
[15,]   14 0.0204 -3.10579 0.125
[16,]   15 0.0204 -3.46202 0.125
[17,]   16 0.0204 -3.81852 0.125
[18,]   17 0.0204 -4.17514 0.125
[19,]   18 0.0204 -4.53181 0.125
[20,]   19 0.0204 -4.88851 0.125
[21,]   20 0.0204 -5.24522 0.125
>   summary(TV)
Oblique rotation method Oblimin Quartimin converged in  21  iterations.
Loadings:
         Factor1 Factor2
NL1      -0.0245 -0.8055
TV2       0.0822 -0.7884
NL3      -0.0194 -0.7847
RTL4      0.6350 -0.1038
RTL5      0.7294 -0.0495
Veronica  0.8518  0.0589
SBS6      0.7504  0.0409
>   
> 
> 
> cleanEx(); ..nameEx <- "Random.Start"
> 
> ### * Random.Start
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Random.Start
> ### Title: Generate a Random Orthogonal Rotation
> ### Aliases: Random.Start
> ### Keywords: multivariate
> 
> ### ** Examples
> 
>    Global.min <- function(A,method,B=10){
+       fv <- rep(0,B)
+       seeds <- sample(1e+7, B)
+       for(i in 1:B){
+         cat(i," ")
+         set.seed(seeds[i])
+         gpout <- GPFoblq(A=A, Random.Start(ncol(A)), method=method)
+         dtab <- dim(gpout$Table)
+         fv[i] <- gpout$Table[dtab[1],2]
+         cat(fv[i], "\n")
+       }
+       cat("Min is ",min(fv),"\n")
+       set.seed(seeds[order(fv)[1]])
+       ans <- GPFoblq(A=A, Random.Start(ncol(A)), method=method)
+       ans
+       }
> 
>    data("Thurstone", package="GPArotation")
> 
>    Global.min(box26,"simplimax",10)
1  0.2532918 
2  0.3305051 
3  0.1439683 
4  Warning in GPFoblq(A = A, Random.Start(ncol(A)), method = method) : 
	 convergence not obtained.1000 iterations used.
0.2531122 
5  0.2473104 
6  Warning in GPFoblq(A = A, Random.Start(ncol(A)), method = method) : 
	 convergence not obtained.1000 iterations used.
0.2807472 
7  0.08037128 
8  0.1748273 
9  0.1054259 
10  0.1312377 
Min is  0.08037128 
Oblique rotation method Simplimax converged.
Loadings:
         [,1]    [,2]     [,3]
 [1,] -0.8313  0.6923 -0.00587
 [2,]  0.5969 -0.3977  1.32555
 [3,] -0.7102 -0.5263  0.07215
 [4,] -0.0545  0.1623  0.91325
 [5,] -1.0013  0.0741  0.00263
 [6,] -0.0383 -0.6190  0.85324
 [7,] -0.4236  0.4008  0.55118
 [8,]  0.2429 -0.1100  1.14838
 [9,] -0.9993  0.3330 -0.02234
[10,] -1.0222 -0.1509  0.03317
[11,]  0.2182 -0.5829  1.07126
[12,] -0.2693 -0.6187  0.60982
[13,] -1.2321  0.8714 -1.15555
[14,]  1.2321 -0.8714  1.15555
[15,] -0.0304  0.9837  0.03266
[16,]  0.0304 -0.9837 -0.03266
[17,]  1.2483  0.0347  1.20460
[18,] -1.2483 -0.0347 -1.20460
[19,]  0.0742  0.0748  1.00772
[20,] -1.0202  0.0358 -0.03427
[21,] -0.0401 -0.6019  0.86072
[22,]  0.0664  0.0654  0.99332
[23,] -0.9781  0.0119 -0.01506
[24,] -0.0336 -0.5700  0.86093
[25,] -0.3951 -0.1407  0.67309
[26,] -0.2818 -0.2499  0.74083

Rotating matrix:
       [,1]   [,2]  [,3]
[1,] -0.371 -0.197 0.702
[2,]  1.417 -0.601 1.263
[3,]  0.176  0.898 0.305

Phi:
       [,1]  [,2]   [,3]
[1,]  1.000 0.163 -0.680
[2,]  0.163 1.000  0.168
[3,] -0.680 0.168  1.000
>    
> 
> 
> cleanEx(); ..nameEx <- "rotations"
> 
> ### * rotations
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rotations
> ### Title: Rotations
> ### Aliases: oblimin quartimin targetT targetQ pstT pstQ oblimax entropy
> ###   quartimax Varimax simplimax bentlerT bentlerQ tandemI tandemII
> ###   geominT geominQ cfT cfQ infomaxT infomaxQ mccammon vgQ.oblimin
> ###   vgQ.quartimin vgQ.target vgQ.pst vgQ.oblimax vgQ.entropy
> ###   vgQ.quartimax vgQ.varimax vgQ.simplimax vgQ.bentler vgQ.tandemI
> ###   vgQ.tandemII vgQ.geomin vgQ.cf vgQ.infomax vgQ.mccammon
> ### Keywords: multivariate
> 
> ### ** Examples
> 
>   data(ability.cov)
>   factanal(factors = 2, covmat = ability.cov, rotation="oblimin")

Call:
factanal(factors = 2, covmat = ability.cov, rotation = "oblimin")

Uniquenesses:
general picture  blocks    maze reading   vocab 
  0.455   0.589   0.218   0.769   0.052   0.334 

Loadings:
        Factor1 Factor2
general  0.386   0.475 
picture          0.646 
blocks           0.896 
maze             0.488 
reading  0.990         
vocab    0.791         

               Factor1 Factor2
SS loadings      1.756   1.688
Proportion Var   0.293   0.281
Cumulative Var   0.293   0.574

Test of the hypothesis that 2 factors are sufficient.
The chi square statistic is 6.11 on 4 degrees of freedom.
The p-value is 0.191 
> 
>   data("Harman", package="GPArotation")
>   qHarman  <- GPForth(Harman8, Tmat=diag(2), method="quartimax")
>   qHarman2 <- quartimax(Harman8) 
> 
>   data("WansbeekMeijer", package="GPArotation")
>   fa.unrotated  <- factanal(factors = 2, covmat=NetherlandsTV, rotation="none")
> 
>   fa.varimax <- factanal(factors = 2, covmat=NetherlandsTV, 
+                 rotation="varimax", control=list(rotate=list(normalize=TRUE)))
>   fa.oblimin <- factanal(factors = 2, covmat=NetherlandsTV,
+                 rotation="oblimin", control=list(rotate=list(normalize=TRUE)))
>   
>   cbind(loadings(fa.unrotated), loadings(fa.varimax), loadings(fa.oblimin))
           Factor1    Factor2   Factor1   Factor2     Factor1     Factor2
NL1      0.6972803 -0.3736554 0.2360221 0.7550574 -0.02448863  0.80550694
TV2      0.7774628 -0.3184149 0.3319439 0.7717834  0.08217889  0.78835099
NL3      0.6832300 -0.3620428 0.2341260 0.7369283 -0.01944302  0.78471128
RTL4     0.6612198  0.2361132 0.6373377 0.2945535  0.63501085  0.10381118
RTL5     0.6972393  0.3026050 0.7096161 0.2723186  0.72938957  0.04951539
Veronica 0.7100285  0.4059509 0.7911239 0.2075079  0.85179157 -0.05889848
SBS6     0.6353584  0.3526947 0.7005266 0.1932262  0.75043563 -0.04089475
> 
>   
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  41.74 0.39 42.29 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')