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> # testing that the print.GPArotation output is identical 
> # for 2 runs of quartimin rotation, that have 2
> # different looking loadings matrices wrt sign and order
> # the print.GPArotation should look identical
> 
> 
>  Sys.getenv("R_LIBS")
[1] "D:\\temp\\Rtmpqiwotp\\RLIBS_256f87557c21"
>  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" 
>  
> require("stats")  
> require("GPArotation")  
> 
> athl <- matrix(c(
+   .73, -.07, .50, .82, -.01, .27,  .77, -.46, -.22,  .78, .17, .03,
+   .77, .41, .13,  .81, -.01, .27,  .71, -.45, -.30,  .82, .12, -.11,
+   .66, -.15, -.45,  .39, .76, -.40), byrow=T,  ncol =3)
> ## z1 gives the results that have the right ordering and sign of the factors
> ## z2 is a random other order and sign
> set.seed(238)
> z1 <- quartimin(athl, Tmat = Random.Start(3))
> head(z1$loadings)
           [,1]        [,2]         [,3]
[1,] -0.9451409  0.05346419  0.180327102
[2,] -0.7725340 -0.14313505 -0.011868009
[3,] -0.1322889 -0.86168891  0.128470606
[4,] -0.5377313 -0.20500970 -0.287529554
[5,] -0.6888492  0.05547964 -0.440716643
[6,] -0.7665208 -0.13863386 -0.009868994
> set.seed(46)
> z2 <- quartimin(athl, Tmat = Random.Start(3))
> head(z2$loadings)
           [,1]         [,2]        [,3]
[1,] -0.9451416 -0.180326159  0.05346510
[2,] -0.7725340  0.011869079 -0.14313424
[3,] -0.1322881 -0.128469679 -0.86168934
[4,] -0.5377307  0.287530600 -0.20500891
[5,] -0.6888486  0.440717717  0.05548088
[6,] -0.7665208  0.009870051 -0.13863307
> 
> # WITHOUT SORTING
> all.ok <- TRUE  
> # are z1 and z2 loadings different? Test at the 5th decimal
> # if tst = T then there are differences (good). if tst = F then no differences (bad)
> tst <- max(z1$loadings - z2$loadings) > 1e-5
> if (! tst) { all.ok <- F}
> # rotation matrix
> tst <- max(z1$Th - z2$Th) > 1e-5
> if (! tst) { all.ok <- F}
> # correlation matrix
> tst <- max(z1$Phi - z2$Phi) > 1e-5
> if (! tst) { all.ok <- F}
> 
> if (! all.ok) stop("some tests FAILED before sorting")
> 
> 
> # NOW WE SORT: z1 to z1s and z2 to z2s
> z1s <- print(z1, sortLoadings = TRUE, rotateMat = TRUE, Table = TRUE)
Oblique rotation method Quartimin converged.
Loadings:
         [,1]    [,2]     [,3]
 [1,]  0.9451 -0.0535 -0.18033
 [2,]  0.7725  0.1431  0.01187
 [3,]  0.1323  0.8617 -0.12847
 [4,]  0.5377  0.2050  0.28753
 [5,]  0.6888 -0.0555  0.44072
 [6,]  0.7665  0.1386  0.00987
 [7,]  0.0150  0.8967 -0.08931
 [8,]  0.4047  0.3792  0.32647
 [9,] -0.1056  0.7915  0.24071
[10,] -0.0155 -0.0165  0.94994

                [,1]  [,2]  [,3]
SS loadings    3.374 2.675 1.528
Proportion Var 0.337 0.268 0.153
Cumulative Var 0.337 0.605 0.758

Phi:
      [,1]  [,2]  [,3]
[1,] 1.000 0.554 0.259
[2,] 0.554 1.000 0.186
[3,] 0.259 0.186 1.000

Rotating matrix:
      [,1]   [,2]   [,3]
[1,] 0.601  0.450  0.200
[2,] 0.220 -0.707  0.868
[3,] 1.043 -0.863 -0.531

Iteration table:
      iter     f log10(s) alpha
 [1,]    0 0.641   0.0671 1.000
 [2,]    1 0.528  -0.3459 0.125
 [3,]    2 0.500  -0.7144 0.250
 [4,]    3 0.483  -0.6656 0.500
 [5,]    4 0.452  -0.3927 1.000
 [6,]    5 0.430  -0.6116 0.250
 [7,]    6 0.406  -0.5591 0.500
 [8,]    7 0.380  -0.5007 0.500
 [9,]    8 0.350  -0.4382 0.500
[10,]    9 0.326  -0.5634 0.250
[11,]   10 0.289  -0.5615 0.500
[12,]   11 0.223  -0.6139 1.000
[13,]   12 0.185  -0.6265 1.000
[14,]   13 0.171  -0.8657 0.500
[15,]   14 0.165  -1.1075 0.500
[16,]   15 0.163  -1.2994 0.500
[17,]   16 0.162  -1.4865 0.500
[18,]   17 0.161  -1.6643 0.500
[19,]   18 0.161  -1.8373 0.500
[20,]   19 0.161  -1.8981 1.000
[21,]   20 0.161  -2.3175 0.250
[22,]   21 0.161  -2.4862 0.500
[23,]   22 0.161  -2.6521 0.500
[24,]   23 0.161  -2.8163 0.500
[25,]   24 0.161  -2.8540 1.000
[26,]   25 0.161  -3.2855 0.250
[27,]   26 0.161  -3.4503 0.500
[28,]   27 0.161  -3.6136 0.500
[29,]   28 0.161  -3.7757 0.500
[30,]   29 0.161  -3.8078 1.000
[31,]   30 0.161  -4.2454 0.250
[32,]   31 0.161  -4.4084 0.500
[33,]   32 0.161  -4.5704 0.500
[34,]   33 0.161  -4.7318 0.500
[35,]   34 0.161  -4.7541 1.000
[36,]   35 0.161  -5.2020 0.250
> z2s <- print(z2, sortLoadings = TRUE, rotateMat = TRUE, Table = TRUE)
Oblique rotation method Quartimin converged.
Loadings:
         [,1]    [,2]     [,3]
 [1,]  0.9451 -0.0535 -0.18033
 [2,]  0.7725  0.1431  0.01187
 [3,]  0.1323  0.8617 -0.12847
 [4,]  0.5377  0.2050  0.28753
 [5,]  0.6888 -0.0555  0.44072
 [6,]  0.7665  0.1386  0.00987
 [7,]  0.0150  0.8967 -0.08930
 [8,]  0.4047  0.3792  0.32647
 [9,] -0.1056  0.7915  0.24071
[10,] -0.0155 -0.0165  0.94994

                [,1]  [,2]  [,3]
SS loadings    3.374 2.675 1.528
Proportion Var 0.337 0.268 0.153
Cumulative Var 0.337 0.605 0.758

Phi:
      [,1]  [,2]  [,3]
[1,] 1.000 0.554 0.259
[2,] 0.554 1.000 0.186
[3,] 0.259 0.186 1.000

Rotating matrix:
      [,1]   [,2]   [,3]
[1,] 0.601  0.450  0.200
[2,] 0.220 -0.707  0.868
[3,] 1.043 -0.863 -0.531

Iteration table:
      iter     f log10(s) alpha
 [1,]    0 0.513    0.159 1.000
 [2,]    1 0.338   -0.187 0.125
 [3,]    2 0.263   -0.455 0.250
 [4,]    3 0.214   -0.568 0.500
 [5,]    4 0.172   -0.726 1.000
 [6,]    5 0.165   -1.001 0.250
 [7,]    6 0.162   -1.334 0.500
 [8,]    7 0.161   -1.612 0.500
 [9,]    8 0.161   -1.840 0.500
[10,]    9 0.161   -2.031 0.500
[11,]   10 0.161   -2.208 0.500
[12,]   11 0.161   -2.377 0.500
[13,]   12 0.161   -2.419 1.000
[14,]   13 0.161   -2.848 0.250
[15,]   14 0.161   -3.016 0.500
[16,]   15 0.161   -3.182 0.500
[17,]   16 0.161   -3.214 1.000
[18,]   17 0.161   -3.647 0.250
[19,]   18 0.161   -3.814 0.500
[20,]   19 0.161   -3.979 0.500
[21,]   20 0.161   -4.143 0.500
[22,]   21 0.161   -4.182 1.000
[23,]   22 0.161   -4.611 0.250
[24,]   23 0.161   -4.775 0.500
[25,]   24 0.161   -4.938 0.500
[26,]   25 0.161   -5.100 0.500
> all.ok <- TRUE  
> # are z1 and z2 loadings different? Test at the 5th decimal
> # if tst = T then there are differences (bad). if tst = F then no differences (good)
> tst <- max(z1s$loadings - z2s$loadings) > 1e-5
> if (tst) { all.ok <- F}
> # rotation matrix
> tst <- max(z1s$Th - z2s$Th) > 1e-5
> if (tst) { all.ok <- F}
> # correlation matrix
> tst <- max(z1s$Phi - z2s$Phi) > 1e-5
> if (tst) { all.ok <- F}
> 
> if (! all.ok) stop("some tests FAILED after sorting")
> 
> #> z1
> #Oblique rotation method Quartimin converged.
> #Loadings:
> #         [,1]    [,2]     [,3]
> # [1,]  0.9451 -0.0535 -0.18033
> # [2,]  0.7725  0.1431  0.01187
> # [3,]  0.1323  0.8617 -0.12847
> # [4,]  0.5377  0.2050  0.28753
> # [5,]  0.6888 -0.0555  0.44072
> # [6,]  0.7665  0.1386  0.00987
> # [7,]  0.0150  0.8967 -0.08931
> # [8,]  0.4047  0.3792  0.32647
> # [9,] -0.1056  0.7915  0.24071
> #[10,] -0.0155 -0.0165  0.94994
> #
> #                [,1]  [,2]  [,3]
> #SS loadings    3.034 2.405 1.401
> #Proportion Var 0.303 0.240 0.140
> #Cumulative Var 0.303 0.544 0.684
> #
> #Phi:
> #      [,1]  [,2]  [,3]
> #[1,] 1.000 0.554 0.259
> #[2,] 0.554 1.000 0.186
> #[3,] 0.259 0.186 1.000
> #> z2
> #Oblique rotation method Quartimin converged.
> #Loadings:
> #         [,1]    [,2]     [,3]
> # [1,]  0.9451 -0.0535 -0.18033
> # [2,]  0.7725  0.1431  0.01187
> # [3,]  0.1323  0.8617 -0.12847
> # [4,]  0.5377  0.2050  0.28753
> # [5,]  0.6888 -0.0555  0.44072
> # [6,]  0.7665  0.1386  0.00987
> # [7,]  0.0150  0.8967 -0.08930
> # [8,]  0.4047  0.3792  0.32647
> # [9,] -0.1056  0.7915  0.24071
> #[10,] -0.0155 -0.0165  0.94994
> #
> #                [,1]  [,2]  [,3]
> #SS loadings    3.034 2.405 1.401
> #Proportion Var 0.303 0.240 0.140
> #Cumulative Var 0.303 0.544 0.684
> #
> #Phi:
> #      [,1]  [,2]  [,3]
> #[1,] 1.000 0.554 0.259
> #[2,] 0.554 1.000 0.186
> #[3,] 0.259 0.186 1.000
> 
> 
> ##########################################################
> # RUNNING A PRINT WITHOUT ERRORS
> ##########################################################
> #  data(ability.cov)
> #  L <- loadings(factanal(factors = 2, covmat=ability.cov))
> #
> #v <- GPFRSoblq(L, eps = 1e-7, method = "oblimin", methodArgs = list(gam = .5), randomStarts = 100)
> #GPArotation:::print.GPArotation(v, rotateMat = T, Table = T)
> #print(v, rotateMat = T, Table = T)
> #
> #GPArotation:::summary.GPArotation(v) 
> #summary(v)
> 
> 
> 
> proc.time()
   user  system elapsed 
   0.15    0.06    0.21