#############################################################
##                        mmtbx.xtriage                    ##
##                                                         ##
##      P.H. Zwart, R.W. Grosse-Kunstleve & P.D. Adams     ##
##                                                         ##
#############################################################
Date 2005-10-19 Time 21:26:24 PDT -0700


##-------------------------------------------##
## WARNING:                                  ##
## Number of residues unspecified            ##
##-------------------------------------------##


Effective parameters: 
scaling.input {
  basic {
    n_residues = None
    n_bases = None
    n_copies_per_asu = None
    n_terms = None
  }
  analyses {
    verbose = 1
    log = "2fiv.log"
  }
  xray_data {
    file_name = "2fiv.mtz"
    labels = "F,SIGF"
    unit_cell = 50.49000168 50.49000168 74.29000092 90 90 120
    space_group = "P 31"
    high_resolution = 0
    low_resolution = 10
  }
}


Symmetry, cell and reflection file content summary

Miller array info: 2fiv.mtz:F,SIGF
Observation type: xray.amplitude
Type of data: double, size=14969
Type of sigmas: double, size=14969
Number of Miller indices: 14969
Anomalous flag: False
Unit cell: (50.49, 50.49, 74.29, 90, 90, 120)
Space group: P 31 (No. 144)
Systematic absences: 0
Centric reflections: 0
Resolution range: 17.6782 1.90013
Completeness in resolution range: 0.896938
Completeness with d_max=infinity: 0.895972

##----------------------------------------------------##
##                    Basic statistics                ##
##----------------------------------------------------##


Matthews coefficient and Solvent content statistics

Number of residues unknown, asuming 50% solvent content

----------------------------------------------------------------
|              Best guess :  200  residues in the asu          |
----------------------------------------------------------------


Maximum likelihood isotropic Wilson scaling 
ML estimate of overall B value of 2fiv.mtz:F,SIGF:
15.75 A**(-2)
Estimated -log of scale factor of 2fiv.mtz:F,SIGF:
 0.41


Maximum likelihood anisotropic Wilson scaling 
ML estimate of overall B_cart value of 2fiv.mtz:F,SIGF:
15.98, -0.00,  0.00
       15.98,  0.00
              15.27
Equivalent representation as U_cif: 
 0.20,  0.10, -0.00
        0.20,  0.00
               0.19

ML estimate of  -log of scale factor of 2fiv.mtz:F,SIGF:
 0.41
Correcting for anisotropy in the data

Some basis intensity statistics follow.



Low resolution completeness analyses 

 The following table shows the completeness
 off the data to 5 Angstrom.
unused:         - 17.6783 [  0/18 ] 0.000
bin  1: 17.6783 - 10.1271 [ 88/90 ] 0.978
bin  2: 10.1271 -  8.3068 [ 88/88 ] 1.000
bin  3:  8.3068 -  7.3423 [ 86/89 ] 0.966
bin  4:  7.3423 -  6.7112 [ 90/93 ] 0.968
bin  5:  6.7112 -  6.2530 [ 80/81 ] 0.988
bin  6:  6.2530 -  5.8989 [ 99/102] 0.971
bin  7:  5.8989 -  5.6134 [ 74/80 ] 0.925
bin  8:  5.6134 -  5.3762 [106/107] 0.991
bin  9:  5.3762 -  5.1746 [ 80/80 ] 1.000
bin 10:  5.1746 -  5.0002 [ 84/85 ] 0.988
unused:  5.0002 -         [  0/0  ]



Mean intensity analyses 
 Analyses of the mean intensity. 
 Inpsired by: Morris et al. (2004). J. Synch. Rad.11, 56-59.
 The following resolution shells are worrisome: 
------------------------------------------------
| d_spacing | z_score | compl. | <Iobs>/<Iexp> |
------------------------------------------------
|    4.874  |   4.90  |   0.98 |     1.730     |
|    4.468  |   4.62  |   0.99 |     1.607     |
|    2.581  |   5.04  |   0.94 |     0.744     |
|    1.968  |   5.06  |   0.73 |     1.517     |
|    1.953  |   7.55  |   0.82 |     1.793     |
------------------------------------------------

 Possible reasons for the presence of the reported
 unexpected low or elevated mean intensity in
 a given resolution bin are : 
 - missing overloaded or weak reflections
 - suboptimal data processing
 - satelite (ice) crystals
 - NCS
 - translational pseudo symmetry (detected elsewhere)
 - outliers (detected elsewhere)
 - ice rings (detected elsewhere)
 - other problems
 Note that the presence of abnormalities 
 in a certain region of reciprocal space might
 confuse the data validation algorithm throughout
 a large region of reciprocal space, even though
 the data is acceptable in those areas. 


Possible outliers 
  Inspired by: Read, Acta Cryst. (1999). D55, 1759-1764

 Acentric reflections:

            None 

 Centric reflections:

            None 


Ice ring related problems

 The following statistics were obtained from ice-ring 
 insensitive resolution ranges 
  mean bin z_score      : 2.33
      ( rms deviation   : 1.37 )
  mean bin completeness : 0.92
     ( rms deviation   : 0.07 )

 The following table shows the z-scores 
 and completeness in ice-ring sensitive areas.
 Large z-scores and high completeness in these 
 resolution ranges might be a reason to re-assess
 your data processsing if ice rings were present.

------------------------------------------------
| d_spacing | z_score | compl. | Rel. Ice int. |
------------------------------------------------
|    3.897  |   1.57  |   0.97 |     1.000     |
|    3.669  |   1.13  |   0.97 |     0.750     |
|    3.441  |   0.30  |   0.98 |     0.530     |
|    2.671  |   1.31  |   0.92 |     0.170     |
|    2.249  |   1.42  |   0.90 |     0.390     |
|    2.072  |   0.41  |   0.87 |     0.300     |
|    1.948  |   2.05  |   0.81 |     0.040     |
|    1.918  |   2.18  |   0.72 |     0.180     |
------------------------------------------------

 Abnormalities in mean intensity or completeness at
 resolution ranges with a relative ice ring intensity
 lower than 0.10 will be ignored.

 No ice ring related problems detected.
 If ice rings were present, the data does not look
 worse at ice ring related d_spacings as compared
 to the rest of the data set 




Basic analyses completed

##----------------------------------------------------##
##                   Twinning Analyses                ##
##----------------------------------------------------##



Using data between 10.00 to 0.00 Angstrom.

Determining possible twin laws.

The following twin laws have been found:

--------------------------------
| Type | Twin law              |
--------------------------------
|   M  | -k,-h,-l              |
|   M  | -h,-k,l               |
|   M  | k,h,-l                |
--------------------------------
M:  Merohedral twin law
PM: Pseudomerohedral twin law

  3 merohedral twin operators found
  0 pseudo-merohedral twin operators found
In total,   3 twin operator were found


Number of centrics  : 0
Number of acentrics : 14877

 Largest patterson peak with length larger then 15 Angstrom 

 Frac. coord.        :   0.332   -0.337    0.448
 Distance to origin  :  44.292
 Height (origin=100) :   9.826
 p_value(height)     :   1.691e-01

   The reported p_value has the following meaning: 
     The probability that a peak of the specified height 
     or larger is found in a Patterson function of a 
     macro molecule that does not have any translational
     pseudo symmetry is equal to  1.691e-01 
     p_values smaller then 0.05 might indicate 
     weak translation pseudo symmetry, or the self vector of 
     a large anomalous scatterer such as Hg, whereas values 
     smaller than 1e-3 are a very strong indication for 
     the presence of translational pseudo symmetry.



Wilson ratio and moments 

Acentric reflections 
   <I^2>/<I>^2    :1.896   (untwinned: 2.000; perfect twin 1.500)
   <F>^2/<F^2>    :0.824   (untwinned: 0.785; perfect twin 0.885)
   <|E^2 - 1|>    :0.678   (untwinned: 0.736; perfect twin 0.541)



NZ test (0<=z<1) to detect twinning and possible translational NCS


-----------------------------------------------
|  Z  | Nac_obs | Nac_theo | Nc_obs | Nc_theo |
-----------------------------------------------
| 0.0 |   0.000 |    0.000 |  0.000 |   0.000 |
| 0.1 |   0.038 |    0.095 |  0.000 |   0.248 |
| 0.2 |   0.112 |    0.181 |  0.000 |   0.345 |
| 0.3 |   0.203 |    0.259 |  0.000 |   0.419 |
| 0.4 |   0.289 |    0.330 |  0.000 |   0.474 |
| 0.5 |   0.369 |    0.394 |  0.000 |   0.520 |
| 0.6 |   0.439 |    0.451 |  0.000 |   0.561 |
| 0.7 |   0.502 |    0.503 |  0.000 |   0.597 |
| 0.8 |   0.558 |    0.551 |  0.000 |   0.629 |
| 0.9 |   0.610 |    0.593 |  0.000 |   0.657 |
| 1.0 |   0.648 |    0.632 |  0.000 |   0.683 |
-----------------------------------------------
| Maximum deviation acentric      :  0.070    |
| Maximum deviation centric       :  0.683    |
|                                             |
| <NZ(obs)-NZ(twinned)>_acentric  : -0.020    |
| <NZ(obs)-NZ(twinned)>_centric   : -0.467    |
-----------------------------------------------


 L test for acentric data

 using difference vectors (dh,dk,dl) of the form: 
(2hp,2kp,2lp)
  where hp, kp, and lp are random signed integers such that 
  2 <= |dh| + |dk| + |dl| <= 8 

  Mean |L|   :0.444  (untwinned: 0.500; perfect twin: 0.375)
  Mean  L^2  :0.268  (untwinned: 0.333; perfect twin: 0.200)

  The distribution of |L| values indicates a twin fraction of
  0.09. Note that this estimate is not as reliable as obtained
  via a britton plot or H-test if twin laws are available. 



---------------------------------------------
 Analysing possible twin law :  -k,-h,-l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.452   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.285   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.048
Estimation of twin fraction via cum. dist. of H: 0.055



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: 0.040
  Correlation: 0.9961

---------------------------------------------
 Analysing possible twin law :  -h,-k,l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.458   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.289   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.042
Estimation of twin fraction via cum. dist. of H: 0.039



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: 0.040
  Correlation: 0.9959

---------------------------------------------
 Analysing possible twin law :  k,h,-l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.103   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.030   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.397
Estimation of twin fraction via cum. dist. of H: 0.419



Britton analyses

  Extrapolation performed on  0.47 < alpha < 0.495 
  Estimated twin fraction: 0.418
  Correlation: 0.9942

------------------------------------------------------------------
Twin analyses summary 

 Twinning tests independent of twin laws 

 Ratio of moments of intensity 
   Intensity ratio                          : 1.896  
   Amplitude ratio                          : 0.824 
     Mahalanobis distance I and F ratio     : 1.687 

 L-test 
   mean |L|                                 : 0.444 
   mean L^2                                 : 0.268 
     Mahalanobis distance of L-test moments : 6.109 

 Detection of translational pseudo symmtery
   Patterson peak height                    : 9.826 (p_value: 1.691e-01)

 Twin law dependent tests 

   Twin law : -k,-h,-l
     estimated twin fraction 
       - via Britton analyses : 0.04
       - via H-test           : 0.05

   Twin law : -h,-k,l
     estimated twin fraction 
       - via Britton analyses : 0.04
       - via H-test           : 0.04

   Twin law : k,h,-l
     estimated twin fraction 
       - via Britton analyses : 0.42
       - via H-test           : 0.42

 Mahalanobis distance: multidimensional equivalent of Z-score.
   Values of the Mahalanobis distance larger then 4 should be 
   seen as an indication that the data does not behave as 
   expected.

 Interpretation of results: 

 No significant pseudotranslation is detected 
 The values of the L-test indicate that the data is twinned.
 As there are twin operators, there is a good possibility
 that your data is actually twinned.

 The data appears to be twinned.
 The largest possible twin fraction is equal to : 0.42
 and might be a good start for density modification or refinement 
 procedures.
------------------------------------------------------------------


$TABLE: Intensity plots:
$GRAPHS
:Intensity plots 
:A:1,2,3,4:
$$
1/resol^2   <I>_smooth_approximation   <I>_via_binning   <I>_expected   $$ 
$$
0.010092   84813.860555   107725.679227   61469.402170
0.014092   50386.275554   37807.674919   48206.790540
0.018092   37700.129071   38712.878518   35453.835206
0.022092   34528.440012   35681.960673   30502.824967
0.026092   37116.239890   33938.428168   30560.429673
0.030092   44724.827551   45959.745045   33702.185782
0.034092   56904.247572   58536.712820   41018.612993
0.038092   74960.970150   59367.119769   52573.383679
0.042092   96700.254144   113423.043803   65567.629071
0.046092   116549.043412   106251.919233   76161.088995
0.050092   124008.763165   131796.391617   82034.143305
0.054092   112461.317024   121506.655273   83344.182560
0.058092   90431.405423   78281.370373   81909.726116
0.062092   74759.504382   82343.322368   79738.497186
0.066092   72724.483739   69423.684176   77982.825399
0.070092   76869.550747   69420.366007   76727.582240
0.074092   76801.629909   86750.657092   75401.280637
0.078092   70722.103619   67845.256427   73362.167493
0.082092   64130.870805   56813.842956   70303.377374
0.086092   61099.653981   67880.633232   66350.495800
0.090092   59976.383723   59424.085680   61919.891648
0.094092   56813.245517   57948.368725   57489.921311
0.098092   50489.598881   45274.297981   53418.211303
0.102092   43589.100810   45517.013320   49867.634736
0.106092   39279.577033   36841.692628   46833.185899
0.110092   38329.185254   36390.870092   44221.878176
0.114092   38955.360650   40181.442063   41933.111439
0.118092   38785.891879   39026.679655   39906.049724
0.122092   36721.047847   37922.189049   38126.611522
0.126092   33395.305374   30681.574023   36606.481250
0.130092   30379.535053   30720.600565   35354.282588
0.134092   28926.387658   26984.197017   34355.772544
0.138092   29066.332596   29982.027655   33570.634678
0.142092   29634.195053   30261.239098   32943.829205
0.146092   29281.231599   31144.220025   32423.444603
0.150092   27715.232126   23796.086681   31975.920986
0.154092   26006.453369   26544.624711   31592.438017
0.158092   25524.980995   25147.430551   31285.006607
0.162092   26489.668531   26956.200545   31075.117495
0.166092   27686.143148   29285.517738   30980.168992
0.170092   27758.437364   27603.635911   31002.882573
0.174092   26686.387257   26488.313027   31127.026907
0.178092   25735.845747   25181.334984   31320.052636
0.182092   25909.276595   25933.080181   31540.791291
0.186092   26777.381164   25986.727617   31748.969709
0.190092   27168.692744   28112.700151   31913.208618
0.194092   26827.221735   25925.160148   32015.199276
0.198092   26797.139867   29438.350955   32049.357392
0.202092   27932.001619   25506.155854   32018.824618
0.206092   29560.648111   29063.278060   31929.731309
0.210092   30247.702912   32781.156077   31785.906692
0.214092   29607.058061   28007.521708   31585.759553
0.218092   28563.026986   26907.115447   31322.108853
0.222092   27914.668480   30223.128993   30984.680311
0.226092   27685.911533   25917.008432   30564.145186
0.230092   27867.786222   28288.364097   30056.188218
0.234092   28269.627401   28750.475338   29464.215462
0.238092   27817.646588   27573.185292   28799.852534
0.242092   26528.518210   25168.536992   28081.132983
0.246092   26913.351905   26739.437092   27328.991921
0.250092   29037.971747   31136.544037   26563.155095
0.254092   30202.027098   28531.992462   25798.631924
0.258092   34768.317791   37982.895623   25043.778658
0.262092   41009.635436   43575.951887   24300.392329
0.266092   33334.279053   26863.273251   23565.689674
0.270092   28582.688582   28880.118492   22835.494374
0.274092   27018.487328   25734.657139   22107.642915
0.276969   27439.013257   31751.814910   21586.674849
$$


$TABLE: Z scores and completeness:
$GRAPHS
:Data sanity and completeness check 
:A:1,2,3:
$$
1/resol^2   Z_score   Completeness   $$ 
$$
0.010092   3.395831   1.000000
0.014092   2.075820   0.975309
0.018092   0.759443   0.989474
0.022092   1.372858   0.969388
0.026092   1.018120   0.974359
0.030092   2.651133   0.937500
0.034092   3.340785   0.992481
0.038092   1.225610   0.992000
0.042092   4.904981   0.979167
0.046092   3.301555   0.986486
0.050092   4.616767   0.987500
0.054092   3.689383   0.960265
0.058092   0.561808   0.969880
0.062092   0.401847   0.994220
0.066092   1.570065   0.972222
0.070092   1.369193   0.994565
0.074092   1.679025   0.966480
0.078092   1.126569   0.972222
0.082092   2.873936   0.946429
0.086092   0.303268   0.984536
0.090092   0.616909   0.970464
0.094092   0.107383   0.974747
0.098092   2.478818   0.962264
0.102092   1.355425   0.981818
0.106092   3.936947   0.959184
0.110092   2.843514   0.945000
0.114092   0.645731   0.966942
0.118092   0.349244   0.988327
0.122092   0.077891   0.968750
0.126092   2.701126   0.953488
0.130092   2.388691   0.920415
0.134092   3.980541   0.938272
0.138092   1.734889   0.949153
0.142092   1.309197   0.921260
0.146092   0.632923   0.910714
0.150092   5.040507   0.940711
0.154092   2.908159   0.913043
0.158092   3.733199   0.940075
0.162092   2.437332   0.885246
0.166092   0.864251   0.889313
0.170092   1.891835   0.909091
0.174092   2.734611   0.882550
0.178092   3.736134   0.877551
0.182092   3.399669   0.901316
0.186092   3.266491   0.922481
0.190092   2.177042   0.898734
0.194092   3.727457   0.876582
0.198092   1.417480   0.895082
0.202092   4.066210   0.910596
0.206092   1.511438   0.867133
0.210092   0.523433   0.879552
0.214092   2.004550   0.870861
0.218092   2.592606   0.882353
0.222092   0.417524   0.883234
0.226092   2.743972   0.819936
0.230092   1.051781   0.882521
0.234092   0.410568   0.867257
0.238092   0.727986   0.869697
0.242092   1.740530   0.772436
0.246092   0.356686   0.803468
0.250092   2.625529   0.891534
0.254092   1.489168   0.723647
0.258092   5.062113   0.732258
0.262092   7.546241   0.819672
0.266092   2.054900   0.809019
0.270092   3.195804   0.733728
0.274092   2.177788   0.722689
0.276969   2.806493   0.787879
$$


$TABLE: <I/sigma_I>:
$GRAPHS
:Signal to noise 
:N:1,2:
$$
1/resol^2   <I/sigma_I>;_Signal_to_noise   $$ 
$$
0.005200   30.770163
0.009200   33.156479
0.013200   33.477735
0.017200   32.235967
0.021200   33.567635
0.025200   31.467681
0.029200   32.046837
0.033200   34.608423
0.037200   31.653351
0.041200   34.453739
0.045200   34.894100
0.049200   35.742967
0.053200   34.915650
0.057200   31.489433
0.061200   31.129788
0.065200   26.039611
0.069200   27.182254
0.073200   29.361454
0.077200   27.324790
0.081200   23.683114
0.085200   23.724281
0.089200   23.283169
0.093200   22.076646
0.097200   17.537109
0.101200   17.854845
0.105200   16.985898
0.109200   16.497645
0.113200   14.627504
0.117200   15.257968
0.121200   15.499009
0.125200   13.298021
0.129200   12.440476
0.133200   12.750368
0.137200   11.786624
0.141200   11.313990
0.145200   11.350585
0.149200   10.302470
0.153200   9.685114
0.157200   9.305349
0.161200   9.877799
0.165200   9.363223
0.169200   9.495903
0.173200   8.464165
0.177200   8.298790
0.181200   9.046569
0.185200   8.368033
0.189200   8.548377
0.193200   7.639412
0.197200   8.423068
0.201200   7.535142
0.205200   7.990868
0.209200   8.319529
0.213200   7.756542
0.217200   6.328327
0.221200   6.884894
0.225200   6.116577
0.229200   7.218828
0.233200   6.634543
0.237200   5.856856
0.241200   6.092357
0.245200   5.414842
0.249200   5.471076
0.253200   5.812401
0.257200   4.533462
0.261200   6.269467
0.265200   4.193380
0.269200   4.432300
0.273200   3.456270
0.277200   4.037086
$$


$TABLE: NZ test:
$GRAPHS
:NZ test, acentric and centric data 
:A:1,2,3,4,5:
$$
z   Acentric_observed   Acentric_untwinned   Centric_observed   Centric_untwinned   $$ 
$$
0.000000   0.000000   0.000000   0.000000   0.000000
0.100000   0.038180   0.095200   0.000000   0.248100
0.200000   0.111783   0.181300   0.000000   0.345300
0.300000   0.203334   0.259200   0.000000   0.418700
0.400000   0.289171   0.329700   0.000000   0.473800
0.500000   0.368892   0.393500   0.000000   0.520500
0.600000   0.439067   0.451200   0.000000   0.561400
0.700000   0.501647   0.503400   0.000000   0.597200
0.800000   0.558379   0.550700   0.000000   0.628900
0.900000   0.609599   0.593400   0.000000   0.657200
1.000000   0.648249   0.632100   0.000000   0.683300
$$


$TABLE: L test,acentric data:
$GRAPHS
:L test, acentric data 
:A:1,2,3,4:
$$
|l|   Observed   Acentric_theory   Acentric_theory,_perfect_twin   $$ 
$$
0.000000   0.000335   0.000000   0.000000
0.020000   0.022533   0.020000   0.029996
0.040000   0.046406   0.040000   0.059968
0.060000   0.068940   0.060000   0.089892
0.080000   0.092227   0.080000   0.119744
0.100000   0.116100   0.100000   0.149500
0.120000   0.140308   0.120000   0.179136
0.140000   0.164265   0.140000   0.208628
0.160000   0.186798   0.160000   0.237952
0.180000   0.211007   0.180000   0.267084
0.200000   0.232451   0.200000   0.296000
0.220000   0.254314   0.220000   0.324676
0.240000   0.274585   0.240000   0.353088
0.260000   0.297537   0.260000   0.381212
0.280000   0.321243   0.280000   0.409024
0.300000   0.345787   0.300000   0.436500
0.320000   0.368655   0.320000   0.463616
0.340000   0.393114   0.340000   0.490348
0.360000   0.417239   0.360000   0.516672
0.380000   0.440359   0.380000   0.542564
0.400000   0.463813   0.400000   0.568000
0.420000   0.487016   0.420000   0.592956
0.440000   0.508209   0.440000   0.617408
0.460000   0.530491   0.460000   0.641332
0.480000   0.552605   0.480000   0.664704
0.500000   0.574887   0.500000   0.687500
0.520000   0.595745   0.520000   0.709696
0.540000   0.619367   0.540000   0.731268
0.560000   0.640978   0.560000   0.752192
0.580000   0.665522   0.580000   0.772444
0.600000   0.686463   0.600000   0.792000
0.620000   0.709583   0.620000   0.810836
0.640000   0.731865   0.640000   0.828928
0.660000   0.751047   0.660000   0.846252
0.680000   0.772072   0.680000   0.862784
0.700000   0.790836   0.700000   0.878500
0.720000   0.811191   0.720000   0.893376
0.740000   0.829871   0.740000   0.907388
0.760000   0.847881   0.760000   0.920512
0.780000   0.864634   0.780000   0.932724
0.800000   0.883649   0.800000   0.944000
0.820000   0.900737   0.820000   0.954316
0.840000   0.918160   0.840000   0.963648
0.860000   0.933909   0.860000   0.971972
0.880000   0.947479   0.880000   0.979264
0.900000   0.959457   0.900000   0.985500
0.920000   0.971101   0.920000   0.990656
0.940000   0.981571   0.940000   0.994708
0.960000   0.989613   0.960000   0.997632
0.980000   0.996231   0.980000   0.999404
$$


$TABLE: Britton plot for twin law -k,-h,-l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.001037   0.000000
0.019802   0.004223   0.000000
0.029703   0.007556   0.000000
0.039604   0.011927   0.000000
0.049505   0.018446   0.009174
0.059406   0.024224   0.018888
0.069307   0.029854   0.028601
0.079208   0.036299   0.038315
0.089109   0.043855   0.048028
0.099010   0.051189   0.057742
0.108911   0.059560   0.067455
0.118812   0.067857   0.077168
0.128713   0.076302   0.086882
0.138614   0.086303   0.096595
0.148515   0.096229   0.106309
0.158416   0.103860   0.116022
0.168317   0.113119   0.125736
0.178218   0.124231   0.135449
0.188119   0.133565   0.145163
0.198020   0.142529   0.154876
0.207921   0.151048   0.164589
0.217822   0.161568   0.174303
0.227723   0.171716   0.184016
0.237624   0.182828   0.193730
0.247525   0.193051   0.203443
0.257426   0.203348   0.213157
0.267327   0.213423   0.222870
0.277228   0.224017   0.232584
0.287129   0.234165   0.242297
0.297030   0.245796   0.252011
0.306931   0.255500   0.261724
0.316832   0.264909   0.271437
0.326733   0.274613   0.281151
0.336634   0.285280   0.290864
0.346535   0.295726   0.300578
0.356436   0.307356   0.310291
0.366337   0.320690   0.320005
0.376238   0.332617   0.329718
0.386139   0.343359   0.339432
0.396040   0.353878   0.349145
0.405941   0.365360   0.358858
0.415842   0.376620   0.368572
0.425743   0.386473   0.378285
0.435644   0.396770   0.387999
0.445545   0.408993   0.397712
0.455446   0.420253   0.407426
0.465347   0.431958   0.417139
0.475248   0.442181   0.426853
0.485149   0.453663   0.436566
$$


$TABLE: H test for possible twin law -k,-h,-l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.046970   0.000000
0.020000   0.073048   0.022469
0.040000   0.091125   0.044938
0.060000   0.109498   0.067407
0.080000   0.129945   0.089877
0.100000   0.145948   0.112346
0.120000   0.170247   0.134815
0.140000   0.188324   0.157284
0.160000   0.204327   0.179753
0.180000   0.227145   0.202222
0.200000   0.245814   0.224691
0.220000   0.265669   0.247160
0.240000   0.281968   0.269630
0.260000   0.302712   0.292099
0.280000   0.325233   0.314568
0.300000   0.345681   0.337037
0.320000   0.364350   0.359506
0.340000   0.384798   0.381975
0.360000   0.402578   0.404444
0.380000   0.418284   0.426914
0.400000   0.438139   0.449383
0.420000   0.460661   0.471852
0.440000   0.479034   0.494321
0.460000   0.501259   0.516790
0.480000   0.523781   0.539259
0.500000   0.545414   0.561728
0.520000   0.569121   0.584198
0.540000   0.591643   0.606667
0.560000   0.609720   0.629136
0.580000   0.634020   0.651605
0.600000   0.650615   0.674074
0.620000   0.671655   0.696543
0.640000   0.689139   0.719012
0.660000   0.711957   0.741481
0.680000   0.731516   0.763951
0.700000   0.752556   0.786420
0.720000   0.773300   0.808889
0.740000   0.798192   0.831358
0.760000   0.817751   0.853827
0.780000   0.838495   0.876296
0.800000   0.861313   0.898765
0.820000   0.881464   0.921235
0.840000   0.902800   0.943704
0.860000   0.922359   0.966173
0.880000   0.938065   0.988642
0.900000   0.952586   1.000000
0.920000   0.968588   1.000000
0.940000   0.979849   1.000000
0.960000   0.987257   1.000000
0.980000   0.997037   1.000000
$$


$TABLE: Britton plot for twin law -h,-k,l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.001040   0.000000
0.019802   0.004160   0.000000
0.029703   0.007503   0.000000
0.039604   0.013001   0.000000
0.049505   0.019018   0.009000
0.059406   0.023772   0.018869
0.069307   0.030458   0.028738
0.079208   0.036327   0.038606
0.089109   0.044202   0.048475
0.099010   0.053191   0.058344
0.108911   0.061734   0.068213
0.118812   0.070723   0.078081
0.128713   0.078969   0.087950
0.138614   0.087958   0.097819
0.148515   0.097244   0.107687
0.158416   0.105564   0.117556
0.168317   0.115593   0.127425
0.178218   0.125102   0.137293
0.188119   0.134314   0.147162
0.198020   0.143303   0.157031
0.207921   0.152292   0.166899
0.217822   0.161875   0.176768
0.227723   0.172201   0.186637
0.237624   0.180522   0.196505
0.247525   0.192333   0.206374
0.257426   0.204814   0.216243
0.267327   0.216180   0.226111
0.277228   0.226358   0.235980
0.287129   0.236907   0.245849
0.297030   0.248050   0.255717
0.306931   0.260085   0.265586
0.316832   0.270857   0.275455
0.326733   0.280663   0.285324
0.336634   0.291435   0.295192
0.346535   0.303172   0.305061
0.356436   0.312681   0.314930
0.366337   0.324493   0.324798
0.376238   0.336305   0.334667
0.386139   0.347225   0.344536
0.396040   0.358740   0.354404
0.405941   0.370032   0.364273
0.415842   0.381844   0.374142
0.425743   0.391056   0.384010
0.435644   0.401530   0.393879
0.445545   0.414085   0.403748
0.455446   0.426863   0.413616
0.465347   0.439566   0.423485
0.475248   0.451675   0.433354
0.485149   0.464973   0.443222
$$


$TABLE: H test for possible twin law -h,-k,l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.019614   0.000000
0.020000   0.049629   0.021690
0.040000   0.075483   0.043380
0.060000   0.094502   0.065070
0.080000   0.117385   0.086761
0.100000   0.142645   0.108451
0.120000   0.162853   0.130141
0.140000   0.183952   0.151831
0.160000   0.198217   0.173521
0.180000   0.219614   0.195211
0.200000   0.241308   0.216901
0.220000   0.259138   0.238592
0.240000   0.277266   0.260282
0.260000   0.300149   0.281972
0.280000   0.318574   0.303662
0.300000   0.339079   0.325352
0.320000   0.356315   0.347042
0.340000   0.379198   0.368732
0.360000   0.397028   0.390423
0.380000   0.413373   0.412113
0.400000   0.436256   0.433803
0.420000   0.459138   0.455493
0.440000   0.479049   0.477183
0.460000   0.501337   0.498873
0.480000   0.518574   0.520563
0.500000   0.544428   0.542254
0.520000   0.569094   0.563944
0.540000   0.587519   0.585634
0.560000   0.605944   0.607324
0.580000   0.627043   0.629014
0.600000   0.646062   0.650704
0.620000   0.666568   0.672394
0.640000   0.683804   0.694085
0.660000   0.704309   0.715775
0.680000   0.727786   0.737465
0.700000   0.747103   0.759155
0.720000   0.771174   0.780845
0.740000   0.790193   0.802535
0.760000   0.808915   0.824225
0.780000   0.832689   0.845915
0.800000   0.854383   0.867606
0.820000   0.878752   0.889296
0.840000   0.902823   0.910986
0.860000   0.921545   0.932676
0.880000   0.938782   0.954366
0.900000   0.950669   0.976056
0.920000   0.965527   0.997746
0.940000   0.980386   1.000000
0.960000   0.987816   1.000000
0.980000   0.997028   1.000000
$$


$TABLE: Britton plot for twin law k,h,-l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.000000   0.000000
0.019802   0.000000   0.000000
0.029703   0.000000   0.000000
0.039604   0.000000   0.000000
0.049505   0.000218   0.000000
0.059406   0.000291   0.000000
0.069307   0.000291   0.000000
0.079208   0.000363   0.000000
0.089109   0.000436   0.000000
0.099010   0.000944   0.000000
0.108911   0.001598   0.000000
0.118812   0.002179   0.000000
0.128713   0.002542   0.000000
0.138614   0.003487   0.000000
0.148515   0.004359   0.000000
0.158416   0.005085   0.000000
0.168317   0.005957   0.000000
0.178218   0.006610   0.000000
0.188119   0.007482   0.000000
0.198020   0.008717   0.000000
0.207921   0.010824   0.000000
0.217822   0.012131   0.000000
0.227723   0.013947   0.000000
0.237624   0.016272   0.000000
0.247525   0.018233   0.000000
0.257426   0.020848   0.000000
0.267327   0.023754   0.000000
0.277228   0.027677   0.000000
0.287129   0.030583   0.000000
0.297030   0.033852   0.000000
0.306931   0.038137   0.000000
0.316832   0.041624   0.000000
0.326733   0.046346   0.000000
0.336634   0.052085   0.000000
0.346535   0.058187   0.000000
0.356436   0.064870   0.000000
0.366337   0.073660   0.000000
0.376238   0.082740   0.000000
0.386139   0.093055   0.000000
0.396040   0.101119   0.000000
0.405941   0.112959   0.000000
0.415842   0.126689   0.000000
0.425743   0.140564   0.037477
0.435644   0.159523   0.087239
0.445545   0.182333   0.137000
0.455446   0.207831   0.186762
0.465347   0.237978   0.236523
0.475248   0.281854   0.286285
0.485149   0.339024   0.336047
$$


$TABLE: H test for possible twin law k,h,-l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.070754   0.000000
0.020000   0.273573   0.122822
0.040000   0.438036   0.245644
0.060000   0.551068   0.368466
0.080000   0.627779   0.491288
0.100000   0.682115   0.614110
0.120000   0.730350   0.736933
0.140000   0.772773   0.859755
0.160000   0.797763   0.982577
0.180000   0.822752   1.000000
0.200000   0.842801   1.000000
0.220000   0.854424   1.000000
0.240000   0.869243   1.000000
0.260000   0.884643   1.000000
0.280000   0.900625   1.000000
0.300000   0.914572   1.000000
0.320000   0.922127   1.000000
0.340000   0.931135   1.000000
0.360000   0.941305   1.000000
0.380000   0.947988   1.000000
0.400000   0.951475   1.000000
0.420000   0.954090   1.000000
0.440000   0.958739   1.000000
0.460000   0.965131   1.000000
0.480000   0.968618   1.000000
0.500000   0.971233   1.000000
0.520000   0.973267   1.000000
0.540000   0.976173   1.000000
0.560000   0.979079   1.000000
0.580000   0.981694   1.000000
0.600000   0.984019   1.000000
0.620000   0.985762   1.000000
0.640000   0.986924   1.000000
0.660000   0.988377   1.000000
0.680000   0.989830   1.000000
0.700000   0.991573   1.000000
0.720000   0.991864   1.000000
0.740000   0.993898   1.000000
0.760000   0.994479   1.000000
0.780000   0.995932   1.000000
0.800000   0.996804   1.000000
0.820000   0.998838   1.000000
0.840000   0.999128   1.000000
0.860000   0.999419   1.000000
0.880000   0.999419   1.000000
0.900000   0.999709   1.000000
0.920000   1.000000   1.000000
0.940000   1.000000   1.000000
0.960000   1.000000   1.000000
0.980000   1.000000   1.000000
$$