#   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  

sortFac <- function(x){  # Based on Fungible faSort 
  vx <- order(colSums(x$loadings^2), decreasing = TRUE)
  Dsgn <- diag(sign(colSums(x$loadings^3))) [ , vx]
  x$Th <- x$Th %*% Dsgn 
  x$loadings <- x$loadings %*% Dsgn
  if ("Phi" %in% names(x)) { 
    x$Phi <- diag(1/diag(Dsgn)) %*% x$Phi %*% Dsgn
    }
  x 
} 


  data(ability.cov)
  L <- loadings(factanal(factors = 2, covmat=ability.cov))
  set.seed(100)
 tst <- sortFac(Varimax(L, normalize=FALSE, randomStarts = 100))$loadings
 if( 0.001 < max(abs(varimax(L, normalize=FALSE)$loadings - tst))){
    cat("Calculated difference exceeds tolerance\n")
    cat("difference:\n")
    print(varimax(L, normalize=FALSE)$loadings - tst, digits=18)
    all.ok <- FALSE  
    } 

  set.seed(100)
 tst <- sortFac(Varimax(L, normalize=TRUE, randomStarts = 100))$loadings
 if( 0.01 < max(abs(varimax(L, normalize=TRUE)$loadings - tst))) {
    cat("Calculated difference exceeds tolerance\n")
    cat("difference:\n")
    print(varimax(L, normalize=TRUE)$loadings - tst, digits=18)
    all.ok <- FALSE  
    } 

 set.seed(99)
  v <- sortFac(oblimin(L, eps=1e-8, randomStarts = 100))$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  
    } 

  set.seed(98)
  v <- sortFac(quartimin(L, eps=1e-8, randomStarts = 100))$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  
    } 

#  # This fails with the old Random.Start
#  set.seed(97)
#  v <- sortFac(targetT(L, Target=matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
#               eps=1e-5, randomStarts = 100))$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  
#    } 

#  # This fails with the old Random.Start
# Random starts get to a lower f value (1.8) which is a mismatch to the tst matrix 
# generated without random starts. Its f value is 5.6
# removed the test 
#  set.seed(96)
#  v <- sortFac(targetQ(L, Target=matrix(c(rep(1,3),rep(0,6),rep(1,3)), 6,2),
#               eps=1e-5, randomStarts = 100))$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  
#    } 




#    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 <- sortFac(entropy(L, maxit=3000, eps=1e-5, randomStarts = 100))$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  
    } 

  fuzz <- 1e-4  # 4th decimal differences
  set.seed(110)
  v <- sortFac(quartimax(L, eps=1e-7, randomStarts = 100))$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  
    } 
 
   set.seed(110)
  v <- sortFac(GPFRSorth(L, eps = 1e-7, method = "quartimax", randomStarts = 100))$loadings
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 9-GPFRSorth. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 
     
    

 set.seed(90)
  v <- sortFac(Varimax(L, eps=1e-8, randomStarts = 100))$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  
    } 
    
    set.seed(90)
  v <- sortFac(GPFRSorth(L, eps = 1e-7, method = "varimax", randomStarts = 100))$loadings
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 10-GPFRSorth. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 

    

  set.seed(89)
  v <- sortFac(simplimax(L, eps=1e-5, randomStarts = 100))$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[,2:1]))) {
    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  
    } 
    
    set.seed(89)
  v <- sortFac(GPFRSoblq(L, eps = 1e-5, method = "simplimax", randomStarts = 100))$loadings
  if( fuzz < max(abs(v - tst[,2:1]))) {
    cat("Calculated value is not the same as test value in test rotations 11-GPFRSoblq. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  set.seed(88)
  v <- sortFac(bentlerT(L, eps=1e-8, randomStarts = 100))$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  
    } 
    
  set.seed(88)
   v <- sortFac(GPFRSorth(L, eps = 1e-7, method = "bentler", randomStarts = 100))$loadings
  if( fuzz < max(abs(v - tst))) {
    cat("Calculated value is not the same as test value in test rotations 12-GPFRSorth. Value:\n")
    print(v, digits=18)
    cat("difference:\n")
    print(v - tst, digits=18)
    all.ok <- FALSE  
    } 


  set.seed(97)
  v <- sortFac(bentlerQ(L, eps=1e-8, randomStarts = 100))$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  
    } 

  fuzz <- 1e-5
  set.seed(85)
  v <- sortFac(tandemI(L, eps=1e-6, maxit = 1000, randomStarts = 100))$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  
    } 


  fuzz <- 1e-5
  set.seed(84)
  v <- sortFac(tandemII(L, eps=1e-5, randomStarts = 100))$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  
    } 

  fuzz <- 1e-6
  set.seed(81)
  v <- sortFac(geominT(L, eps=1e-5, randomStarts = 100))$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  
    } 

  fuzz <- 1e-6
  set.seed(80)
  v <- sortFac(geominQ(L, eps=1e-5, randomStarts = 100))$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  
    } 

  set.seed(70)
  v <- sortFac(cfT(L, eps=1e-8, randomStarts = 100))$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  
    } 

  set.seed(60)
  v <- sortFac(cfQ(L, eps=1e-8, randomStarts = 100))$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  
    } 

  fuzz <- 1e-5
  set.seed(55)
  v <- sortFac(infomaxT(L, eps=1e-5, randomStarts = 100))$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  
    } 

  fuzz <- 1e-5
  set.seed(50)
  v <- sortFac(infomaxQ(L, eps=1e-5, randomStarts = 100))$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  
    } 

 set.seed(40)
  v <- sortFac(mccammon(L, eps=1e-5, randomStarts = 100))$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))
  tst <- tst[, 2:1]
  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  
    } 



   set.seed(35)
   v <- sortFac(oblimax(Harman8, eps=1e-5, randomStarts = 100))$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  
    } 
	  
 
cat("tests completed.\n")


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