tests/rotations.R

In GPArotation: Gradient Projection Factor Rotation

#   Tests here only compare against values computed previously with this code,
#   to ensure there was no accidental change. It would be better to have
#   comparisons with known correct values.

# Test for oblimax is commented out as it appears to be  unstable.


 Sys.getenv("R_LIBS")
 library()
 require("GPArotation")
 search()
 Sys.info()

require("stats")  
require("GPArotation")  

fuzz <- 1e-6 
all.ok <- TRUE  


  data(ability.cov)
  L <- loadings(factanal(factors = 2, covmat=ability.cov))
  

 if( 0.001 < max(abs(varimax(L, normalize=FALSE)$loadings -
          Varimax(L, normalize=FALSE)$loadings))) {
    cat("Calculated difference exceeds tolerance\n")
    cat("difference:\n")
    print(varimax(L, normalize=FALSE)$loadings -
          Varimax(L, normalize=FALSE)$loadings, digits=18)
    all.ok <- FALSE  
    } 

 if( 0.01 < max(abs(varimax(L, normalize=TRUE)$loadings -
          Varimax(L, normalize=TRUE, eps=1e-5)$loadings))) {
    cat("Calculated difference exceeds tolerance\n")
    cat("difference:\n")
    print(varimax(L, normalize=TRUE)$loadings -
          Varimax(L, normalize=TRUE, eps=1e-5)$loadings, digits=18)
    all.ok <- FALSE  
    } 


  v <- oblimin(L, eps=1e-8)$loadings 
  tst <- t(matrix(c(
           0.3863615904740822504,  0.4745127741495974161,
          -0.0110059418769087539,  0.6458720769633764514,
          -0.0262926272350604423,  0.8961141105684561348,
          -0.0180200526810754824,  0.4882928281695405048,
           0.9900944939102318543, -0.0370718282544326011,
           0.7905657274265397438,  0.0526109550054999417
      ), 2, 6))
 
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 1. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 

  v <- oblimin(L, gam = 1, eps=1e-8)$loadings 
  tst <- t(matrix(c(
  	 0.2160827,  0.5403732,
 	-0.4787025,  1.0224006,
  	-0.6800410,  1.4244177,
 	-0.3758706,  0.7781390,
	 1.4517362, -0.5873946,
	 1.1002585, -0.3396290
      ), 2, 6))
 
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 1-gam=1. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 

  v <- oblimin(L, gam = .1, eps=1e-8)$loadings 
  tst <- t(matrix(c(
	 0.37893531,  0.47408606,
	-0.02465543,  0.65257986,
	-0.04530330,  0.90557045,
	-0.02840333,  0.49349573,
	 0.99740452, -0.05088932,
	 0.79467442,  0.04241284
      ), 2, 6))
 
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 1-gam=.1. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 



  v <- quartimin(L, eps=1e-8)$loadings
  tst <- t(matrix(c(
           0.3863615904740822504,  0.4745127741495974161,
          -0.0110059418769087539,  0.6458720769633764514,
          -0.0262926272350604423,  0.8961141105684561348,
          -0.0180200526810754824,  0.4882928281695405048,
           0.9900944939102318543, -0.0370718282544326011,
           0.7905657274265397438,  0.0526109550054999417
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 2. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- targetT(L, Target=matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
               eps=1e-5)$loadings 
  tst <- t(matrix(c(
  	  0.551529228817982942, 0.4905002767031292898,
  	  0.217748645523411000, 0.6027046291262584399,
  	  0.291173432863349457, 0.8348885228488550636,
  	  0.154994397662456290, 0.4544843569140373241,
  	  0.969702339393929247, 0.0850652965070581996,
  	  0.803390575440818822, 0.1448091121037717866
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 3. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 

  v <- targetT(L = L, Target=matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
               eps=1e-5)$loadings 
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 3L. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- targetQ(L, Target=matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
               eps=1e-5)$loadings  
  tst <- t(matrix(c(
  	  0.735795682866631218, 0.565351705145453853,
  	  0.433590223819374398, 0.664644550038417159,
  	  0.589924557708411568, 0.920006940799857786,
  	  0.317543426981046928, 0.500590650032113116,
  	  1.021758247914384077, 0.155121528590726393,
  	  0.872521244896209747, 0.208735706420634437
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 4. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 

  v <- targetQ(L = L, Target=matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
               eps=1e-5)$loadings  
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 4L. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


 # Does not converge even with maxit=10000, but the loadings matrix is not
 #  changing. Possibly the gradient is extremely large even very close to opt.
  v <- pstT(L, W = matrix(c(rep(.4,6),rep(.6,6)), 6,2),
           Target= matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
               maxit=1000, eps=1e-5)$loadings     
  tst <- t(matrix(c(
          0.37067889993474656407, 0.638257130653133720,
          0.01855112570739854416, 0.640564749523800270,
          0.01576132191496706567, 0.884065831441111172,
          0.00524531003824213384, 0.480158078874985073,
          0.89458633399812259590, 0.383762977265515448,
          0.71793428958051475064, 0.388556883222951677
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 5. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 

  v <- pstT(L = L, W = matrix(c(rep(.4,6),rep(.6,6)), 6,2),
           Target= matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
               maxit=1000, eps=1e-5)$loadings     
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 5L. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 



 # Does not converge even with maxit=10000, but the loadings matrix is not
 #  changing. Possibly the gradient is extremely large even very close to opt.
  v <- pstQ(L, W = matrix(c(rep(.4,6),rep(.6,6)), 6,2),
           Target= matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
               maxit=1000, eps=1e-5)$loadings     
  tst <- t(matrix(c(
          0.573125161748393785, 0.700868331877288475,
          0.214899397066479453, 0.681727425525818886,
          0.286558275327103040, 0.940272379393286339,
          0.152257795885557295, 0.510481967637567036,
          1.029289798076480578, 0.462598702071116141,
          0.850691132520651205, 0.456859727346562328
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 6. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    }
     
    v <- pstQ(L = L, W = matrix(c(rep(.4,6),rep(.6,6)), 6,2),
           Target= matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
               maxit=1000, eps=1e-5)$loadings     
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 6L. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    }


#    oblimax
# this is test value on one computer
#  tst <- t(matrix(c(
#	    -8111059.94622692652,  8111060.62253121007,
#	     1495036.43465861562, -1495035.79614594672,
#	     2331634.63904705830, -2331633.75893370388,
#	     1356735.91680212389, -1356735.43916810025,
#	   -23187491.19758165255, 23187491.68068471923,
#	   -18357040.58573083207, 18357041.05348757654
#      ), 2, 6))
#
# this is test value on another computer
#  tst <- t(matrix(c(
#      2694770.06630349346, -2694769.38999920478,
#      -496701.45733913727,   496702.09585180727,
#      -774647.63529061736,   774648.51540397422,
#      -450753.43529273639,   450753.91292676108,
#      7703672.48495316971, -7703672.00185009185,
#      6098832.71036116872, -6098832.24260441773
#      ), 2, 6))
#
#  this does not converge on all platforms and has large differences possible a mistake ???
#  v <- oblimax(L, eps=1e-5)$loadings  
#  if( fuzz < max(abs(v - tst))) {
#    cat("Calculated value is not the same as test value in test rotations 7. Value:\n")
#    print(v, digits=18)
#    cat("difference:\n")
#    print(v - tst, digits=18)
#    all.ok <- FALSE  
#    } 


  v <- entropy(L, maxit=3000, eps=1e-5)$loadings  
  tst <- t(matrix(c(
	  0.528292107548243184, 0.515443945340967824,
	  0.189686511729033253, 0.612116304198454975,
          0.252311894464850861, 0.847442931117894815,
          0.133843268148035738, 0.461156452364903380,
          0.964740133927989407, 0.129750551769587635,
          0.795847094000000532, 0.181751199795689433
      ), 2, 6))

  if( 0.01 < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 8. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- quartimax(L, eps=1e-5)$loadings
  tst <- t(matrix(c(
  	  0.534714740804540178, 0.508778102568043678,
  	  0.197348140750149392, 0.609689309353509956,
  	  0.262919828098457153, 0.844212045390758559,
  	  0.139616102327241837, 0.459441658926639795,
  	  0.966291466215733252, 0.117641548844535412,
  	  0.798063848020893585, 0.171756193883937508
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 9. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- Varimax(L, eps=1e-8)$loadings  
  tst <- t(matrix(c(
          0.515866523962843160, 0.527879475961036904,
          0.175054634278874244, 0.616460231981747930,
          0.232057748479543163, 0.853211588623112749,
          0.122822468397975171, 0.464213243286899446,
          0.961376376417989453, 0.152689863976982837,
          0.791292800869773050, 0.200653429940987366
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 10. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- simplimax(L, eps=1e-5)$loadings
  tst <- t(matrix(c(
  	   0.3384175759313114429, 0.508414890494446547464,
  	  -0.0654601124161610648, 0.670992229004664153535,
  	  -0.1016231721735353366, 0.930535379393095940515,
  	  -0.0589933707274080121, 0.506904360351960181497,
  	   0.9733094402675376289, 0.000234046050254643859,
  	   0.7702037184085044341, 0.085651123319384916965
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 11. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- bentlerT(L, eps=1e-8)$loadings 
  tst <- t(matrix(c(
          0.523583611303327312, 0.520226117818945788,
          0.184113022124463677, 0.613815719643687197,
          0.244596116053327067, 0.849702038129718673,
          0.129644684715025493, 0.462354355134084738,
          0.963520501269179652, 0.138517057902201340,
          0.794161628656258278, 0.188979901644201559
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 12. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- bentlerQ(L, eps=1e-8)$loadings 
  tst <- t(matrix(c(
           0.3801726240258240241,  0.4741208368044214638,
          -0.0223632969057368826,  0.6514196922540864687,
          -0.0421105927111659756,  0.9039359851665277334,
          -0.0266594447192576613,  0.4925968005718689424,
           0.9961524457620027917, -0.0485973498906049697,
           0.7939648477384558811,  0.0440983921679098251
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 13. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- tandemI(L, eps=1e-5)$loadings  
  tst <- t(matrix(c(
       0.615424480780047745,  0.4074649925368262759,
       0.300894306348887419,  0.5658002819054848143,
       0.406455233467338028,  0.7852483408305571677,
       0.217785179074990981,  0.4279590047675180808,
       0.971977129465111611, -0.0530960591067626969,
       0.815800376450207976,  0.0295946184147908228
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 14. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 



  v <- tandemII(L, eps=1e-5)$loadings 
  tst <- t(matrix(c(
      0.512160139332842212, 0.531476249107136312,
      0.170736763115044710, 0.617670057812827134,
      0.226081850628144149, 0.854814488884392154,
      0.119571200821562001, 0.465061309851099225,
      0.960284416460420398, 0.159413208985883820,
      0.789869387186175276, 0.206185467095899383
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 15. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- geominT(L, eps=1e-5)$loadings  
  tst <- t(matrix(c(
  	  0.572197044101002361, 0.4662247895688098054,
  	  0.243573415560656120, 0.5927388411683653935,
  	  0.326956608263186954, 0.8215352639437966120,
  	  0.174476792179181994, 0.4473668997335142894,
  	  0.972471249855535680, 0.0431091626026945812,
  	  0.808894688433769660, 0.1099794466209375043
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 16. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- geominQ(L, eps=1e-5)$loadings  
  tst <- t(matrix(c(
           0.39672053553904490508,  0.4713295988080449250,
           0.00424452688463150020,  0.6389466007374070555,
          -0.00510976786312981532,  0.8864521406378518265,
          -0.00646959173137159373,  0.4830101828530461994,
           0.98709860078485589518, -0.0318959930081098297,
           0.79011178369962709045,  0.0558689642678330683
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 17. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- bigeominT(L, eps = 1e-5, delta = 0.01)$loadings  
  tst <- t(matrix(c(
	0.735864675930537948,  0.0572554836159610558,
	0.537832587849186305,  0.3484299786828288781,
	0.736693622718023078,  0.4889819217894930681,
	0.398234350199199783,  0.2683070932862005598,
	0.823835376232448180, -0.5185113350380095021,
 	0.727481839163037991, -0.3703731487890759011
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 16-bigeominT. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- bigeominQ(L, eps = 1e-5, delta = 0.01)$loadings  
  tst <- t(matrix(c(
	0.735864459785110725,  0.0572566968425438083,
	0.537831272508815683,  0.3484308654124375071,
	0.736691776787216535,  0.4889831363831567135,
	0.398233337326754422,  0.2683077498589007681,
	0.823837333630433988, -0.5185099767738823306,
	0.727483237333638733, -0.3703719493837349663
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 17-bigeominQ. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- cfT(L, eps=1e-8)$loadings	
  tst <- t(matrix(c(
          0.534721263659975854, 0.508771247100584523,
          0.197355957387199576, 0.609686779159006154,
          0.262930651479430233, 0.844208674501022327,
          0.139621992686633722, 0.459439868910532512,
          0.966292974385164483, 0.117629160286744874,
          0.798066049992627313, 0.171745962120156664
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 18. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- cfQ(L, eps=1e-8)$loadings	
  tst <- t(matrix(c(
           0.3863615904740822504,  0.4745127741495974161,
          -0.0110059418769087539,  0.6458720769633764514,
          -0.0262926272350604423,  0.8961141105684561348,
          -0.0180200526810754824,  0.4882928281695405048,
           0.9900944939102318543, -0.0370718282544326011,
           0.7905657274265397438,  0.0526109550054999417
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 19. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- infomaxT(L, eps=1e-5)$loadings 
  tst <- t(matrix(c(
  	  0.495330443338021176, 0.547195361446864537,
  	  0.151384273205308784, 0.622695868320644275,
  	  0.199304253086364791, 0.861451466010626055,
  	  0.105004533733904976, 0.468565194910632365,
  	  0.954843809781045660, 0.189293503899924942,
  	  0.783052579543945471, 0.230726576980168713
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 20. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- infomaxQ(L, eps=1e-5)$loadings 
  tst <- t(matrix(c(
  	   0.39327554287862442894,  0.4693137508305071925,
  	  -0.00319802321222481794,  0.6422985517185823001,
  	  -0.01549245038490981718,  0.8912279460026399924,
  	  -0.01214605901641467763,  0.4856544522916727002,
  	   0.99260028929193111491, -0.0433225495465055510,
  	   0.79356458059567791530,  0.0471559021503157039
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 21. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- mccammon(L, eps=1e-5)$loadings 
  tst <- t(matrix(c(
        0.4293472299617892007, 0.600363196582340275,
        0.0790140496845253004, 0.635943490060206229,
        0.0992523811009183854, 0.878618107277518656,
        0.0506062164774049028, 0.477512622702450096,
        0.9268544198491108776, 0.297488850382792269,
        0.7514463663627769519, 0.318958389348199534
      ), 2, 6))

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 22. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


###### ADDED IN NOVEMBER 2022 FOR EQUAMAX, PARSIMAX, VARIMIN, OBLIMAX

  data(Thurstone)
  v <- equamax(box26, eps=1e-5)$loadings
  tst <- t(matrix(c(
	0.511813618717971597,  0.1252460667724786814,  0.835031881099661200,
	0.211275278125612587,  0.9469860693462274215,  0.024701038786419674,
	0.923671387190205140,  0.1861505968810791833, -0.278366886980007111,
	0.414270797796799317,  0.7243752493532077397,  0.530526346393166759,
	0.927099794400001564,  0.1710560637343615797,  0.314400690653154735,
	0.685509679739711331,  0.6873945075387188908, -0.212674093365320949,
	0.500975325417812756,  0.4985944480056956341,  0.693100497576226382,
	0.350251174602310256,  0.8631423492204841619,  0.303299191676876356,
	0.809196181501955492,  0.1468111894018074293,  0.540855816747015439,
	1.051940508364259674,  0.2023337382785123650,  0.126016765617061266,
	0.528246625368315792,  0.8145581663496035407, -0.154555803579673606,
	0.791784749686200273,  0.5353191515116044741, -0.254010464723911089,
	0.283760830721282831, -0.7132278971933163625,  0.633221728633476699,
    -0.283760830721282831,  0.7132278971933163625, -0.633221728633476699,
    -0.351981708826951678,  0.0145585781278812498,  0.920862598031950474,
	0.351981708826951678, -0.0145585781278812498, -0.920862598031950474,
    -0.641238077659381234,  0.7340358583767647715,  0.211813801195267382,
	0.641238077659381234, -0.7340358583767647715, -0.211813801195267382,
	0.370916272566192251,  0.7781992933002486179,  0.457012011497068604,
	0.943267697340363864,  0.1458935486092693412,  0.269085717994103968,
	0.683769139477491628,  0.6932804480935084168, -0.193612975261152009,
	0.375506314902942506,  0.7683789003013250518,  0.444462454027040654,
	0.921697465732450816,  0.1542330203892136042,  0.244709944799956780,
	0.664806997738585315,  0.6918110118942031317, -0.165931249557543792,
	0.748952844572093657,  0.5985308972371030656,  0.239842451746804020,
	0.716556890444816297,  0.6343221919993241587,  0.139425892477791219
   ), 3, 26))
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 22. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    }    
 ### SAME FOR CRAWFORD FERGUSON WITH KAPPA = m / (2 * p) = 3 / (2 * 26) 
  v <- cfT(box26, kappa = (3 / (2 * 26)), eps=1e-5)$loadings
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 22. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    }    


  v <- parsimax(box26, eps=1e-5)$loadings
  tst <- t(matrix(c(  
	0.7201835790622810318, -0.2820790149262949464,  0.6137467244615277817,
    -0.0679423851913938670,  0.6010788795762025405,  0.7590243822315081434,
	0.6707172136894012926,  0.7174085874409354968, -0.0277909684381195121,
	0.3564975652920873705,  0.2169149780725644350,  0.8964682806594965747,
	0.8905375652375422391,  0.2961288407436278303,  0.3269136806262873951,
	0.3419238671745732927,  0.8395902605853544642,  0.4072361273101923196,
	0.5551801796495600128,  0.0181442676741417341,  0.8193941381745735164,
	0.1791815177720131602,  0.4232257028261393605,  0.8651329309165379788,
	0.8735154515073240145,  0.0707778916688399651,  0.4481498031114935499,
	0.9254209439635597834,  0.5018907196720771013,  0.2347334274887991901,
	0.1871266535649374341,  0.7975561080494565358,  0.5434380093797205324,
	0.4642991413806251688,  0.8329607560592182658,  0.2619421428072832847,
	0.6793187635833454197, -0.7070938474525871875, -0.1694942722875707464,
    -0.6793187635833454197,  0.7070938474525871875,  0.1694942722875707464,
    	0.0126413340577520572, -0.7959999181796318934,  0.5816488003350992475,
    -0.0126413340577520572,  0.7959999181796318934, -0.5816488003350992475,
    -0.7005089039174136056, -0.0349340740508546910,  0.7091733821870598309,
	0.7005089039174136056,  0.0349340740508546910, -0.7091733821870598309,
	0.2764675266718980007,  0.2782887989292237019,  0.8933946782281918519,
	0.8957285854821546156,  0.3212930506383097073,  0.2790825626255922787,
	0.3455615085575033385,  0.8287155760723180498,  0.4236528505493507568,
	0.2788032457489866833,  0.2837361452757249936,  0.8779069142135194070,
	0.8654448252950356357,  0.3331277242202841382,  0.2706070467039994321,
	0.3390107603224090660,  0.7999236919074760310,  0.4396564471388281214,
	0.5855440811683275681,  0.5029973433114328651,  0.6171108503586539840,
	0.5106729412991620753,  0.5782224406112924653,  0.5832066153589001711
   ), 3, 26))
   
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 22. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    }    
 ### SAME FOR CRAWFORD FERGUSON WITH KAPPA = (m - 1) / (p + m - 2) = (3 -1) / (26 + 3 - 2) 
  v <- cfT(box26, kappa=( (3-1)/(26+3-2) ), eps=1e-5)$loadings
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 22. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    }    

   data(Harman, package= "GPArotation")
   v <- varimin(Harman8, eps=1e-5)$loadings
  tst <- t(matrix(c(
	0.800626657046876855, -0.452452158825595752,
	0.783606930490612252, -0.524447498313301397,
	0.742635936060292656, -0.522609669324872517,
	0.768357486963803682, -0.455227165519225097,
	0.818696625686402668,  0.444445536696790211,
	0.702064973637186673,  0.410429985249392060,
	0.623283524595303340,  0.401857745935120247,
	0.668480210595655877, 0.287458184858228272
	  ), 2, 8))
	  
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 22. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 




   v <- oblimax(Harman8, eps=1e-5)$loadings
  tst <- t(matrix(c(
  		0.93395421734409445058, -0.0302013026726007383,
		0.99243032312927881300, -0.1121899246869615951,
		0.96509469978483286567, -0.1322258547171115683,
		0.91647702431117861188, -0.0502569243958834178,
		0.08441855308346873921,  0.8875309317276611765,
		0.04427084251510177149,  0.7907585046311147448,
		0.00332736511424391868,  0.7399752420126202157,
		0.14133359391312094733,  0.6483050831171799366
	  ), 2, 8))
	  
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 22. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 
    
 # TAKEN FROM THE EXAMPLES IN THE DOCUMENTATION OF echelon
	  
 data(WansbeekMeijer)
 fa.unrotated  <- factanal(factors = 2, covmat=NetherlandsTV, rotation="none")
 v <- echelon(fa.unrotated$loadings)$loadings
 tst <- matrix(c(
		0.7910866, 0.000000000,
		0.8356693, 0.086562877,
		0.7732175, 0.003599155,
		0.4712891, 0.520430204,
		0.4716313, 0.596050663,
		0.4340904, 0.693182608,
		0.3934293, 0.610972389
   ), ncol = 2, nrow = 7, byrow=7)

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 23. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 

# TAKEN FROM THE EXAMPLES IN THE DOCUMENTATION OF eiv

 v <- eiv(fa.unrotated$loadings)$loadings
 tst <- matrix(c(
	 	 1.0000000, 0.0000000,
		 0.0000000, 1.0000000,
		 0.9334902, 0.0415785,
		-5.7552381, 6.0121639,
		-6.6776277, 6.8857539,
		-7.9104168, 8.0078509,
		-6.9585766, 7.0581340
   ), ncol = 2, nrow = 7, byrow=7)

  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 24. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 

# BIFACTOR

  data(WansbeekMeijer)
  fa.unrotated  <- factanal(factors = 3, covmat=NetherlandsTV, rotation="none")
  v <- bifactorT(fa.unrotated$loadings)$loadings

 tst <- matrix(c(
	0.605259846207760410,  0.50926282550276680272, -0.0326441696928007064,
	0.674848533008883589,  0.49892997353743967492,  0.0360559565502543422,
	0.585307624074672961,  0.50452427555859225006, -0.0116655363009391944,
	0.569143997010692737,  0.07907134469847305891,  0.4496106087464453172,
	0.639591951170676909, -0.00317621525167442742,  0.3903956610664964244,
	0.644285080202307459, -0.06194060671151470354,  0.4889273316625122323,
	0.894466584777320994, -0.44135797428894490979, -0.0115183403900823399
   ), ncol = 3, nrow = 7, byrow=7)
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations bifactorT. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  v <- bifactorQ(fa.unrotated$loadings)$loadings

 tst <- matrix(c(
	0.639628269247016989,  0.4617887681341789063, -0.03408526722627130967,
	0.708202536330854282,  0.4531948277009248405,  0.03509478386512845938,
	0.619356995328652293,  0.4604997427039814184, -0.01303680319918767982,
	0.572539420889668138,  0.0819716834028682007,  0.45225086629811012129,
	0.637128483915923693, -0.0107264127434737802,  0.39334646255480443244,
	0.637511978242973232, -0.0601392817604798208,  0.49259101012935263553,
	0.861232867683719872, -0.5044079449050349329, -0.00751942773799910234
   ), ncol = 3, nrow = 7, byrow=7)
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations bifactorQ. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


   
cat("tests completed.\n")


if (! all.ok) stop("some tests FAILED")