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> #Example from: Gradient Projection Algorithms and Software for 
> #  Arbitrary Rotation Criteria in Factor Analysis.
> #  by Coen A. Bernaards and Robert I. Jennrich
> #  Website: http://www.stat.ucla.edu/research
> 
>  Sys.getenv("R_LIBS")
[1] "D:\\temp\\RtmpAj55YZ\\RLIBS_2d3e42b45675f"
>  library()
>  require("GPArotation")
Loading required package: GPArotation
>  search()
 [1] ".GlobalEnv"          "package:GPArotation" "package:stats"      
 [4] "package:graphics"    "package:grDevices"   "package:utils"      
 [7] "package:datasets"    "package:methods"     "Autoloads"          
[10] "package:base"       
>  Sys.info()
       sysname        release        version       nodename        machine 
     "Windows"   "Server x64"  "build 20348"     "CRANWIN3"       "x86-64" 
         login           user effective_user 
        "CRAN"         "CRAN"         "CRAN" 
> 
> 
> fuzz <- 1e-5 # using  eps=1e-5 these tests do not do better than this
> all.ok <- TRUE  
> 
> #  quartimax (orthogonal) rotation of Harman's 8 physical variables.
> 
> data("Harman", package="GPArotation")
> 
> qHarman  <- GPForth(Harman8, Tmat=diag(2), method="quartimax")
> qHarman2 <- quartimax(Harman8) 
> 
>  if( fuzz < max(abs(qHarman$loadings - qHarman2$loadings))) {
+     cat("Calculated value is not the same as test value in test Harman 1. Value:\n")
+     print(qHarman$loadings, digits=18)
+     cat("difference:\n")
+     print(qHarman$loadings - qHarman2$loadings, digits=18)
+     all.ok <- FALSE  
+     } 
> 
> #qHarman$Th - qHarman2$Th
> 
> # with eps=1e-8
> # tst <- t(matrix(c(
> #  0.898754567491920398, 0.194823580226859222,
> #  0.933943406208487592, 0.129748657024604030,
> #  0.902131483644799892, 0.103864268239045668,
> #  0.876508251941102934, 0.171284220753554678,
> #  0.315572019798302239, 0.876476069451083251,
> #  0.251123191235179066, 0.773488941629975613,
> #  0.198007116064591759, 0.714678376605717203,
> #  0.307857241091366252, 0.659334451631046314
> #  ), 2, 8))
> 
> # with eps=1e-5
>  tst <- t(matrix(c(
+   0.898755404698461491, 0.194819718009510034,
+   0.933943963768413821, 0.129744643590955028,
+   0.902131929972106672, 0.103860391510923730,
+   0.876508987992224209, 0.171280454135453869,
+   0.315575786273609882, 0.876474713336210853,
+   0.251126515144778573, 0.773487862471829213,
+   0.198010187248201075, 0.714677525703678707,
+   0.307860074444663512, 0.659333128670876345
+    ), 2, 8))
> 
>  if( fuzz < max(abs(qHarman$loadings - tst ))) {
+     cat("Calculated value is not the same as test value in test Harman 2. Value:\n")
+     print(qHarman$loadings, digits=18)
+     cat("difference:\n")
+     print(qHarman$loadings - tst, digits=18)
+     all.ok <- FALSE  
+     } 
> 
> # with eps=1e-8
> # tst <- t(matrix(c(
> #   0.790828307905322436, 0.612038060430562525,
> #  -0.612038060430562525, 0.790828307905322214
> #  ), 2, 2))
> 
> # with eps=1e-5
>  tst <- t(matrix(c(
+    0.790830938007507367, 0.612034662000581764,
+   -0.612034662000581764, 0.790830938007507145
+   ), 2, 2))
>  
>  if( fuzz < max(abs(qHarman$Th - tst ))) {
+     cat("Calculated value is not the same as test value in test Harman 3. Value:\n")
+     print(qHarman$Th, digits=18)
+     cat("difference:\n")
+     print(qHarman$Th - tst, digits=18)
+     all.ok <- FALSE  
+     } 
> 
> 
> 
> 
> 
> #  quartimin (oblique) rotation of Harman's 8 physical variables.
> 
> qminHarman  <- GPFoblq(Harman8, Tmat=diag(2), method="quartimin")
> qminHarman2 <- quartimin(Harman8) 
> 
>  if( fuzz < max(abs(qminHarman$loadings - qminHarman2$loadings))) {
+     cat("Calculated value is not the same as test value in test Harman 4. Value:\n")
+     print(qminHarman$loadings, digits=18)
+     cat("difference:\n")
+     print(qminHarman$loadings - qminHarman2$loadings, digits=18)
+     all.ok <- FALSE  
+     } 
> 
> 
> # with eps=1e-8
> # tst <- t(matrix(c(
> #   0.8918217697289939627,  0.0560146456758183961,
> #   0.9536799985772628219, -0.0232460005406671701,
> #   0.9291498623396581280, -0.0465027396531852502,
> #   0.8766828510822184395,  0.0336582451338717017,
> #   0.0136988312985193428,  0.9250013826349388069,
> #  -0.0172668087945964319,  0.8212535444941218010,
> #  -0.0524468998178311899,  0.7649536381341245361,
> #   0.0858880630098148856,  0.6831160953442911854
> #   ),2, 8))					
> 
> # with eps=1e-5
>  tst <- t(matrix(c(
+    0.8918219293548808047,  0.0560145122875230911,
+    0.9536799846795966928, -0.0232460559140742311,
+    0.9291497958388006406, -0.0465027685653178480,
+    0.8766829604751505967,  0.0336581364763500201,
+    0.0137008854716444972,  0.9250004106413580729,
+   -0.0172649861805529957,  0.8212526839806429946,
+   -0.0524452035885302342,  0.7649528396536503516,
+    0.0858895830186393733,  0.6831153711863455769
+    ),2, 8))				       
> 					       
>  if( fuzz < max(abs(qminHarman$loadings - tst ))) {
+     cat("Calculated value is not the same as test value in test Harman 5. Value:\n")
+     print(qminHarman$loadings, digits=18)
+     cat("difference:\n")
+     print(qminHarman$loadings - tst, digits=18)
+     all.ok <- FALSE  
+     } 
> 
> 
> # with eps=1e-8
> # tst <- t(matrix(c(
> #  1.000000000000000000, 0.472747617396915065,
> #  0.472747617396915065, 1.000000000000000000
> #   ),2, 2))				       
> 
> # with eps=1e-5
>  tst <- t(matrix(c(
+   1.000000000000000222, 0.472745958387102538,
+   0.472745958387102538, 1.000000000000000000
+    ),2, 2))				       
> 					       
>  if( fuzz < max(abs(qminHarman$Phi - tst ))) {
+     cat("Calculated value is not the same as test value in test Harman 6. Value:\n")
+     print(qminHarman$Phi, digits=18)
+     cat("difference:\n")
+     print(qminHarman$Phi - tst, digits=18)
+     all.ok <- FALSE  
+     } 
> 
> 
> # with eps=1e-8
> # tst <- t(matrix(c(
> #   0.878125245495924522, 0.836723841642554422,
> #  -0.478430823863515542, 0.547625065922776710
> #   ),2, 2))				       
> 
> # with eps=1e-5
>  tst <- t(matrix(c(
+    0.878125280760480686, 0.836722770276292271,
+   -0.478430759137962514, 0.547626702874473570
+    ),2, 2))				       
> 					       
>  if( fuzz < max(abs(qminHarman$Th - tst ))) {
+     cat("Calculated value is not the same as test value in test Harman 7. Value:\n")
+     print(qminHarman$Th, digits=18)
+     cat("difference:\n")
+     print(qminHarman$Th - tst, digits=18)
+     all.ok <- FALSE  
+     } 
> 
> 
> cat("tests completed.\n")
tests completed.
> 
> if (! all.ok) stop("some tests FAILED")
> 
> 
> proc.time()
   user  system elapsed 
   0.17    0.10    0.28