#############################################################
##                        mmtbx.xtriage                    ##
##                                                         ##
##      P.H. Zwart, R.W. Grosse-Kunstleve & P.D. Adams     ##
##                                                         ##
#############################################################
Date 2005-10-19 Time 21:29:25 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 = "questionmark.log"
  }
  xray_data {
    file_name = "questionmark.mtz"
    labels = "FP,SIGFP"
    unit_cell = 99.5 60.90000153 70.95999908 90 134.5 90
    space_group = "C 1 2 1"
    high_resolution = 0
    low_resolution = 10
  }
}


Symmetry, cell and reflection file content summary

Miller array info: questionmark.mtz:FP,SIGFP
Observation type: xray.amplitude
Type of data: double, size=30744
Type of sigmas: double, size=30744
Number of Miller indices: 30744
Anomalous flag: False
Unit cell: (99.5, 60.9, 70.96, 90, 134.5, 90)
Space group: C 1 2 1 (No. 5)
Systematic absences: 0
Centric reflections: 1119
Resolution range: 28.2939 1.68081
Completeness in resolution range: 0.890098
Completeness with d_max=infinity: 0.889918

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


Matthews coefficient and Solvent content statistics

Number of residues unknown, asuming 50% solvent content

----------------------------------------------------------------
|              Best guess :  281  residues in the asu          |
----------------------------------------------------------------


Maximum likelihood isotropic Wilson scaling 
ML estimate of overall B value of questionmark.mtz:FP,SIGFP:
13.82 A**(-2)
Estimated -log of scale factor of questionmark.mtz:FP,SIGFP:
-1.69


Maximum likelihood anisotropic Wilson scaling 
ML estimate of overall B_cart value of questionmark.mtz:FP,SIGFP:
21.41,  0.00, -0.37
       12.32,  0.00
              10.96
Equivalent representation as U_cif: 
 0.20, -0.00,  0.09
        0.16,  0.00
               0.14

ML estimate of  -log of scale factor of questionmark.mtz:FP,SIGFP:
-1.67
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:         - 28.2943 [  0/8  ] 0.000
bin  1: 28.2943 - 10.6002 [129/144] 0.896
bin  2: 10.6002 -  8.4885 [127/135] 0.941
bin  3:  8.4885 -  7.4377 [134/141] 0.950
bin  4:  7.4377 -  6.7679 [129/136] 0.949
bin  5:  6.7679 -  6.2885 [135/139] 0.971
bin  6:  6.2885 -  5.9213 [110/118] 0.932
bin  7:  5.9213 -  5.6272 [144/151] 0.954
bin  8:  5.6272 -  5.3840 [122/127] 0.961
bin  9:  5.3840 -  5.1780 [129/132] 0.977
bin 10:  5.1780 -  5.0004 [126/133] 0.947
unused:  5.0004 -         [  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> |
------------------------------------------------
|    1.954  |   5.06  |   0.88 |     1.329     |
|    1.883  |   4.77  |   0.88 |     0.796     |
|    1.730  |   5.80  |   0.69 |     1.422     |
------------------------------------------------

 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:

-----------------------------------------------------------------
| d_space |      H     K     L |  |E|  | p(wilson) | p(extreme) |
-----------------------------------------------------------------
|   1.729 |    -56,    8,   29 |  9.23 |  0.00e+00 |   0.00e+00 |
|   2.658 |     -1,    9,   18 |  3.71 |  1.06e-06 |   3.10e-02 |
|   2.361 |      0,   14,   18 |  3.80 |  5.49e-07 |   1.61e-02 |
|   2.658 |      1,    9,   17 |  3.80 |  5.54e-07 |   1.62e-02 |
-----------------------------------------------------------------

 p(wilson)  : 1-(1-exp[-|E|^2]) 
 p(extreme) : 1-(1-exp[-|E|^2])^(n_acentrics)
 p(wilson) is the probability that an E-value of the specified
 value would be observed when it would selected at random from
 the given data set.
 p(extreme) is the probability that the largest |E| value is 
 larger or equal than the observed largest |E| value.

 Both measures can be used for outlier detection. p(extreme)
 takes into account the size of the dataset.


 Centric reflections:

            None 


Ice ring related problems

 The following statistics were obtained from ice-ring 
 insensitive resolution ranges 
  mean bin z_score      : 1.54
      ( rms deviation   : 1.00 )
  mean bin completeness : 0.91
     ( rms deviation   : 0.15 )

 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  |   1.19  |   0.98 |     1.000     |
|    3.669  |   2.54  |   0.98 |     0.750     |
|    3.441  |   1.95  |   0.99 |     0.530     |
|    2.671  |   0.60  |   0.97 |     0.170     |
|    2.249  |   1.01  |   0.95 |     0.390     |
|    2.072  |   0.68  |   0.93 |     0.300     |
|    1.948  |   2.28  |   0.90 |     0.040     |
|    1.918  |   4.10  |   0.89 |     0.180     |
|    1.883  |   1.97  |   0.87 |     0.030     |
|    1.721  |   0.56  |   0.68 |     0.020     |
------------------------------------------------

 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              |
--------------------------------
|  PM  | -h,-k,h+l             |
|  PM  | -h-2*l,-k,l           |
|  PM  | -h-2*l,k,h+l          |
--------------------------------
M:  Merohedral twin law
PM: Pseudomerohedral twin law

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


Number of centrics  : 1090
Number of acentrics : 29496

 Largest patterson peak with length larger then 15 Angstrom 

 Frac. coord.        :   0.179    0.264    0.296
 Distance to origin  :  22.188
 Height (origin=100) :   8.485
 p_value(height)     :   2.807e-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  2.807e-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    :2.251   (untwinned: 2.000; perfect twin 1.500)
   <F>^2/<F^2>    :0.790   (untwinned: 0.785; perfect twin 0.885)
   <|E^2 - 1|>    :0.724   (untwinned: 0.736; perfect twin 0.541)


Centric reflections 
   <I^2>/<I>^2    :2.867   (untwinned: 3.000; perfect twin 2.000)
   <F>^2/<F^2>    :0.689   (untwinned: 0.637; perfect twin 0.785)
   <|E^2 - 1|>    :0.991   (untwinned: 0.968; perfect twin 0.736)



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 |   0.078 |    0.095 |  0.144 |   0.248 |
| 0.2 |   0.170 |    0.181 |  0.239 |   0.345 |
| 0.3 |   0.254 |    0.259 |  0.343 |   0.419 |
| 0.4 |   0.330 |    0.330 |  0.421 |   0.474 |
| 0.5 |   0.398 |    0.394 |  0.479 |   0.520 |
| 0.6 |   0.460 |    0.451 |  0.521 |   0.561 |
| 0.7 |   0.515 |    0.503 |  0.557 |   0.597 |
| 0.8 |   0.562 |    0.551 |  0.586 |   0.629 |
| 0.9 |   0.608 |    0.593 |  0.622 |   0.657 |
| 1.0 |   0.647 |    0.632 |  0.656 |   0.683 |
-----------------------------------------------
| Maximum deviation acentric      :  0.017    |
| Maximum deviation centric       :  0.106    |
|                                             |
| <NZ(obs)-NZ(twinned)>_acentric  : +0.003    |
| <NZ(obs)-NZ(twinned)>_centric   : -0.051    |
-----------------------------------------------


 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|   :0.482  (untwinned: 0.500; perfect twin: 0.375)
  Mean  L^2  :0.312  (untwinned: 0.333; perfect twin: 0.200)

  The distribution of |L| values indicates a twin fraction of
  0.01. 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 :  -h,-k,h+l
---------------------------------------------


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

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

mean |H| : 0.090   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.021   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.410
Estimation of twin fraction via cum. dist. of H: 0.427



Britton analyses

  Extrapolation performed on  0.47 < alpha < 0.495 
  Estimated twin fraction: 0.414
  Correlation: 0.9961

---------------------------------------------
 Analysing possible twin law :  -h-2*l,-k,l
---------------------------------------------


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

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

mean |H| : 0.481   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.317   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.019
Estimation of twin fraction via cum. dist. of H: 0.022



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: 0.011
  Correlation: 0.9998

---------------------------------------------
 Analysing possible twin law :  -h-2*l,k,h+l
---------------------------------------------


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

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

mean |H| : 0.483   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.318   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.017
Estimation of twin fraction via cum. dist. of H: 0.016



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: 0.013
  Correlation: 0.9996

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

 Twinning tests independent of twin laws 

 Ratio of moments of intensity 
   Intensity ratio                          : 2.251  
   Amplitude ratio                          : 0.790 
     Mahalanobis distance I and F ratio     : 5.357 

 L-test 
   mean |L|                                 : 0.482 
   mean L^2                                 : 0.312 
     Mahalanobis distance of L-test moments : 1.802 

 Detection of translational pseudo symmtery
   Patterson peak height                    : 8.485 (p_value: 2.807e-01)

 Twin law dependent tests 

   Twin law : -h,-k,h+l
     estimated twin fraction 
       - via Britton analyses : 0.41
       - via H-test           : 0.43

   Twin law : -h-2*l,-k,l
     estimated twin fraction 
       - via Britton analyses : 0.01
       - via H-test           : 0.02

   Twin law : -h-2*l,k,h+l
     estimated twin fraction 
       - via Britton analyses : 0.01
       - via H-test           : 0.02

 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 data does not appear to be twinned

 The data does not appear to be twinned as judged from the 
 L-test. 
 The estimated twin fractions via the britton test do however
 indicate a symmetry relation between possible twin related
 intensities. As the data does not apear to be twinned, one
 can interpret this as origination from a 2-fold NCS axis
 parallel to the putative twin axis or that the spacegroup
 is too low. It might be usefull to refine a putative twin fraction
 during refinement and/or re-assess your data processing.
------------------------------------------------------------------


$TABLE: Intensity plots:
$GRAPHS
:Intensity plots 
:A:1,2,3,4:
$$
1/resol^2   <I>_smooth_approximation   <I>_via_binning   <I>_expected   $$ 
$$
0.010024   168399.025942   183006.871991   115383.293421
0.014024   102868.685937   92615.482606   90799.458479
0.018024   65403.469728   66647.304471   66699.213958
0.022024   49918.405270   48503.523082   57199.727753
0.026024   49052.040009   45039.330027   57201.147298
0.030024   60073.394738   62450.678931   62978.157433
0.034024   83015.156360   81341.822422   76535.909564
0.038024   106114.296224   117052.355835   98078.110549
0.042024   122547.652206   110343.438645   122437.025271
0.046024   139778.289568   147999.013512   142407.150132
0.050024   161635.533899   149288.684237   153568.896195
0.054024   178272.507657   193250.129575   156144.283414
0.058024   178797.977853   179945.035049   153510.218028
0.062024   165173.820342   175934.653322   149442.238659
0.066024   149770.188885   135630.829167   146133.789363
0.070024   142718.106321   141103.739224   143773.457542
0.074024   144130.581792   139700.991797   141302.108349
0.078024   146796.766515   162933.066779   137511.897288
0.082024   143739.658862   130620.197620   131814.226105
0.086024   133098.229396   141093.203910   124431.964844
0.090024   117863.749866   111476.675750   116139.406742
0.094024   102761.591486   94678.679872   107834.046701
0.098024   91402.785009   101256.876236   100191.435544
0.102024   85067.454591   83123.973713   93522.874590
0.106024   82843.050726   75201.932822   87823.194940
0.110024   82451.989340   78449.708149   82919.625891
0.114024   81379.870425   89291.502844   78622.992816
0.118024   78019.727107   77133.348863   74817.764198
0.122024   72385.841249   70998.627516   71476.308880
0.126024   65968.413055   65672.265286   68620.158740
0.130024   60747.079767   55341.921882   66265.953149
0.134024   57965.086641   59435.323073   64387.876382
0.138024   57465.024843   54384.104384   62911.111625
0.142024   57987.011483   63785.476064   61732.748668
0.146024   58134.785477   59266.882661   60755.168771
0.150024   57271.897661   51972.414661   59914.765968
0.154024   55742.246424   56469.008936   59194.242717
0.158024   54370.188136   57193.296689   58615.589052
0.162024   53723.240991   51800.825125   58218.978354
0.166024   53724.309570   50449.111795   58037.325329
0.170024   53852.185127   61383.307938   58076.298013
0.174024   53684.867740   49720.168356   58306.083365
0.178024   53302.507232   52012.370342   58666.121986
0.182024   53227.918345   53923.254615   59079.416880
0.186024   53976.078450   54027.037676   59470.354380
0.190024   55585.911577   59830.927655   59779.779753
0.194024   57498.971106   51687.620916   59972.962546
0.198024   58869.122454   63287.129139   60039.085415
0.202024   59071.920004   60924.548924   59983.843157
0.206024   58064.744421   54887.620160   59818.715347
0.210024   56384.159816   53784.230836   59551.011618
0.214024   54819.569681   57128.873644   59177.941505
0.218024   53980.833347   53475.684987   58686.202660
0.222024   53990.125690   52030.953857   58056.587382
0.226024   54425.301356   56123.078950   57271.522588
0.230024   54528.065369   53296.853406   56322.713066
0.234024   53609.843612   53424.199763   55216.274170
0.238024   51507.851253   54274.998456   53973.740933
0.242024   48847.355328   45373.405529   52628.741263
0.246024   46844.785199   47745.289976   51220.465726
0.250024   46583.413606   42563.492965   49785.966358
0.254024   48107.687000   52954.221478   48353.550642
0.258024   50029.196609   45251.884637   46939.093074
0.262024   50196.115863   60541.481286   45546.145867
0.266024   47216.239629   39591.776795   44169.594559
0.270024   41731.820488   38953.046443   42801.604974
0.274024   36213.541853   33969.747398   41438.013033
0.278024   33136.268301   36416.759373   40083.257444
0.282024   32998.492383   30855.818442   38752.430353
0.286024   34128.649540   34066.403705   37469.866842
0.290024   34626.938694   34573.222207   36264.666128
0.294024   34362.777408   34536.440413   35164.371808
0.298024   34542.265132   37245.976786   34188.521815
0.302024   35264.519332   34326.236490   33343.798509
0.306024   34675.494082   29318.738840   32622.077398
0.310024   31791.132487   35037.083329   32001.915453
0.314024   29103.247059   28661.888248   31453.140197
0.318024   29486.017677   27212.321468   30943.424323
0.322024   30939.004635   31659.407303   30445.249193
0.326024   29960.551181   31266.649914   29941.585591
0.330024   30133.770397   27924.295492   29428.958858
0.334024   35103.029137   41132.356800   28917.223642
0.338024   35421.184201   29325.675316   28426.181131
0.342024   30068.322986   31836.113179   27979.927877
0.346024   29862.345755   27682.674614   27600.347508
0.350024   26760.672413   26182.047769   27301.323906
0.353967   28274.774725   40791.157106   27087.573088
$$


$TABLE: Z scores and completeness:
$GRAPHS
:Data sanity and completeness check 
:A:1,2,3:
$$
1/resol^2   Z_score   Completeness   $$ 
$$
0.010024   3.280524   0.932692
0.014024   0.182054   0.934959
0.018024   0.008008   0.971014
0.022024   1.927001   0.950704
0.026024   3.086916   0.947977
0.030024   0.099355   0.953488
0.034024   0.729520   0.961326
0.038024   2.129748   0.960000
0.042024   1.436185   0.977064
0.046024   0.491214   0.975610
0.050024   0.386301   0.986607
0.054024   2.655526   0.967890
0.058024   2.247107   0.992308
0.062024   2.182538   0.965517
0.066024   1.188207   0.984906
0.070024   0.286458   0.984314
0.074024   0.176930   0.996212
0.078024   2.537041   0.982759
0.082024   0.144410   0.989170
0.086024   1.951734   0.986486
0.090024   0.684319   0.973154
0.094024   2.240512   0.996491
0.098024   0.183302   0.979167
0.102024   2.067364   0.996711
0.106024   2.863791   0.993994
0.110024   0.980172   0.976190
0.114024   2.080222   0.990798
0.118024   0.527899   0.976331
0.122024   0.117510   0.981763
0.126024   0.828752   0.981081
0.130024   3.443614   0.976261
0.134024   1.518381   0.975610
0.138024   2.747870   0.988372
0.142024   0.601387   0.967089
0.146024   0.456879   0.978552
0.150024   2.800974   0.971722
0.154024   0.869583   0.977778
0.158024   0.485427   0.964871
0.162024   2.264641   0.967742
0.166024   2.890781   0.978155
0.170024   1.025759   0.948403
0.174024   3.287080   0.975962
0.178024   2.390341   0.975124
0.182024   1.798290   0.947743
0.186024   1.902261   0.957346
0.190024   0.016310   0.959427
0.194024   3.100626   0.972540
0.198024   1.012935   0.950339
0.202024   0.307253   0.961798
0.206024   1.762713   0.967816
0.210024   2.096763   0.952381
0.214024   0.703434   0.913043
0.218024   1.940970   0.952790
0.222024   2.281540   0.964835
0.226024   0.410648   0.953390
0.230024   1.118997   0.929638
0.234024   0.682004   0.931590
0.238024   0.109278   0.929978
0.242024   3.156628   0.934183
0.246024   1.476537   0.921529
0.250024   3.398516   0.917671
0.254024   1.749013   0.936441
0.258024   0.751066   0.948770
0.262024   5.062247   0.884766
0.266024   2.281354   0.896422
0.270024   1.889926   0.904858
0.274024   4.098923   0.893574
0.278024   1.969034   0.855072
0.282024   4.771101   0.882828
0.286024   1.973167   0.873106
0.290024   0.976268   0.863118
0.294024   0.360420   0.867063
0.298024   1.677734   0.839483
0.302024   0.591135   0.858182
0.306024   2.164760   0.785047
0.310024   1.764431   0.834532
0.314024   1.836376   0.783178
0.318024   2.541946   0.760949
0.322024   0.749753   0.779514
0.326024   0.798603   0.737030
0.330024   0.991699   0.736648
0.334024   5.801358   0.693086
0.338024   0.561644   0.682971
0.342024   2.170146   0.603448
0.346024   0.052988   0.628319
0.350024   0.673888   0.479930
0.353967   1.423052   0.059016
$$


$TABLE: <I/sigma_I>:
$GRAPHS
:Signal to noise 
:N:1,2:
$$
1/resol^2   <I/sigma_I>;_Signal_to_noise   $$ 
$$
0.003249   24.416174
0.007249   25.598709
0.011249   25.454261
0.015249   22.812061
0.019249   23.695558
0.023249   22.141766
0.027249   22.263566
0.031249   22.611437
0.035249   23.691380
0.039249   24.028742
0.043249   23.328410
0.047249   23.306958
0.051249   24.239917
0.055249   25.003059
0.059249   24.333821
0.063249   23.181034
0.067249   23.806597
0.071249   23.022033
0.075249   24.205350
0.079249   23.039533
0.083249   22.843951
0.087249   22.850985
0.091249   20.861467
0.095249   18.807772
0.099249   20.607742
0.103249   19.082594
0.107249   19.972865
0.111249   18.043415
0.115249   18.834631
0.119249   17.702093
0.123249   15.751487
0.127249   15.230856
0.131249   14.604960
0.135249   14.191515
0.139249   14.819705
0.143249   14.000082
0.147249   12.295426
0.151249   12.224045
0.155249   12.874112
0.159249   12.677427
0.163249   11.626442
0.167249   12.290617
0.171249   12.466137
0.175249   11.061669
0.179249   11.154652
0.183249   11.392008
0.187249   11.776009
0.191249   10.371556
0.195249   11.192630
0.199249   10.716541
0.203249   10.637440
0.207249   9.554535
0.211249   9.668762
0.215249   9.603987
0.219249   8.566245
0.223249   8.987583
0.227249   8.955438
0.231249   8.985107
0.235249   8.339926
0.239249   7.656748
0.243249   7.600856
0.247249   6.654798
0.251249   7.177665
0.255249   7.812719
0.259249   7.365125
0.263249   7.355132
0.267249   5.787536
0.271249   5.571320
0.275249   4.745981
0.279249   5.196626
0.283249   4.641506
0.287249   4.662225
0.291249   4.944717
0.295249   3.957761
0.299249   4.635491
0.303249   4.443870
0.307249   3.609955
0.311249   3.707801
0.315249   3.422452
0.319249   2.997699
0.323249   3.192340
0.327249   3.200889
0.331249   2.988640
0.335249   3.270915
0.339249   2.953059
0.343249   3.050675
0.347249   2.667433
0.351249   2.300341
0.355249   1.154918
$$


$TABLE: NZ test:
$GRAPHS
:NZ test, acentric and centric data 
:A:1,2,3,4,5:
$$
z   Acentric_observed   Acentric_untwinned   Centric_observed   Centric_untwinned   $$ 
$$
0.000000   0.000000   0.000000   0.000000   0.000000
0.100000   0.077875   0.095200   0.144037   0.248100
0.200000   0.170023   0.181300   0.239450   0.345300
0.300000   0.253729   0.259200   0.343119   0.418700
0.400000   0.329638   0.329700   0.421101   0.473800
0.500000   0.397851   0.393500   0.478899   0.520500
0.600000   0.459689   0.451200   0.521101   0.561400
0.700000   0.514510   0.503400   0.556881   0.597200
0.800000   0.561703   0.550700   0.586239   0.628900
0.900000   0.607947   0.593400   0.622018   0.657200
1.000000   0.647003   0.632100   0.655963   0.683300
$$


$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   0.001969   0.000000   0.000000
0.020000   0.022563   0.020000   0.029996
0.040000   0.042134   0.040000   0.059968
0.060000   0.063438   0.060000   0.089892
0.080000   0.083875   0.080000   0.119744
0.100000   0.105493   0.100000   0.149500
0.120000   0.125970   0.120000   0.179136
0.140000   0.146761   0.140000   0.208628
0.160000   0.167828   0.160000   0.237952
0.180000   0.188069   0.180000   0.267084
0.200000   0.209529   0.200000   0.296000
0.220000   0.231345   0.220000   0.324676
0.240000   0.251546   0.240000   0.353088
0.260000   0.270565   0.260000   0.381212
0.280000   0.291160   0.280000   0.409024
0.300000   0.313093   0.300000   0.436500
0.320000   0.333609   0.320000   0.463616
0.340000   0.356172   0.340000   0.490348
0.360000   0.376570   0.360000   0.516672
0.380000   0.396771   0.380000   0.542564
0.400000   0.416342   0.400000   0.568000
0.420000   0.439457   0.420000   0.592956
0.440000   0.461548   0.440000   0.617408
0.460000   0.483481   0.460000   0.641332
0.480000   0.502894   0.480000   0.664704
0.500000   0.523331   0.500000   0.687500
0.520000   0.544359   0.520000   0.709696
0.540000   0.563891   0.540000   0.731268
0.560000   0.585430   0.560000   0.752192
0.580000   0.605828   0.580000   0.772444
0.600000   0.627564   0.600000   0.792000
0.620000   0.647923   0.620000   0.810836
0.640000   0.667651   0.640000   0.828928
0.660000   0.688246   0.660000   0.846252
0.680000   0.708171   0.680000   0.862784
0.700000   0.727702   0.700000   0.878500
0.720000   0.747864   0.720000   0.893376
0.740000   0.766332   0.740000   0.907388
0.760000   0.786493   0.760000   0.920512
0.780000   0.806025   0.780000   0.932724
0.800000   0.826068   0.800000   0.944000
0.820000   0.846938   0.820000   0.954316
0.840000   0.866942   0.840000   0.963648
0.860000   0.884111   0.860000   0.971972
0.880000   0.903052   0.880000   0.979264
0.900000   0.922662   0.900000   0.985500
0.920000   0.941445   0.920000   0.990656
0.940000   0.958141   0.940000   0.994708
0.960000   0.973341   0.960000   0.997632
0.980000   0.987793   0.980000   0.999404
$$


$TABLE: Britton plot for twin law -h,-k,h+l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.000502   0.000000
0.019802   0.001254   0.000000
0.029703   0.002007   0.000000
0.039604   0.002544   0.000000
0.049505   0.003297   0.000000
0.059406   0.004013   0.000000
0.069307   0.004909   0.000000
0.079208   0.005841   0.000000
0.089109   0.006772   0.000000
0.099010   0.007883   0.000000
0.108911   0.008922   0.000000
0.118812   0.009818   0.000000
0.128713   0.011001   0.000000
0.138614   0.011968   0.000000
0.148515   0.013258   0.000000
0.158416   0.014512   0.000000
0.168317   0.016125   0.000000
0.178218   0.018024   0.000000
0.188119   0.019350   0.000000
0.198020   0.021392   0.000000
0.207921   0.023399   0.000000
0.217822   0.024868   0.000000
0.227723   0.026732   0.000000
0.237624   0.028953   0.000000
0.247525   0.030637   0.000000
0.257426   0.032895   0.000000
0.267327   0.034973   0.000000
0.277228   0.038234   0.000000
0.287129   0.041531   0.000000
0.297030   0.044863   0.000000
0.306931   0.048017   0.000000
0.316832   0.051313   0.000000
0.326733   0.055972   0.000000
0.336634   0.060988   0.000000
0.346535   0.066972   0.000000
0.356436   0.073028   0.000000
0.366337   0.079908   0.000000
0.376238   0.087720   0.000000
0.386139   0.096535   0.000000
0.396040   0.107751   0.000000
0.405941   0.119934   0.000000
0.415842   0.133945   0.007348
0.425743   0.152686   0.061364
0.435644   0.176013   0.115381
0.445545   0.203963   0.169397
0.455446   0.237575   0.223413
0.465347   0.278138   0.277430
0.475248   0.328376   0.331446
0.485149   0.387824   0.385462
$$


$TABLE: H test for possible twin law -h,-k,h+l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.020784   0.000000
0.020000   0.207841   0.136190
0.040000   0.384003   0.272381
0.060000   0.530352   0.408571
0.080000   0.640866   0.544762
0.100000   0.721565   0.680952
0.120000   0.778614   0.817143
0.140000   0.826059   0.953333
0.160000   0.859600   1.000000
0.180000   0.885831   1.000000
0.200000   0.903462   1.000000
0.220000   0.917652   1.000000
0.240000   0.928546   1.000000
0.260000   0.936143   1.000000
0.280000   0.944170   1.000000
0.300000   0.950763   1.000000
0.320000   0.956353   1.000000
0.340000   0.961227   1.000000
0.360000   0.965384   1.000000
0.380000   0.969182   1.000000
0.400000   0.972049   1.000000
0.420000   0.974342   1.000000
0.440000   0.977066   1.000000
0.460000   0.980076   1.000000
0.480000   0.981509   1.000000
0.500000   0.982656   1.000000
0.520000   0.983946   1.000000
0.540000   0.984949   1.000000
0.560000   0.986526   1.000000
0.580000   0.987673   1.000000
0.600000   0.988676   1.000000
0.620000   0.989680   1.000000
0.640000   0.989823   1.000000
0.660000   0.991113   1.000000
0.680000   0.992116   1.000000
0.700000   0.992833   1.000000
0.720000   0.993120   1.000000
0.740000   0.993406   1.000000
0.760000   0.994266   1.000000
0.780000   0.995126   1.000000
0.800000   0.996130   1.000000
0.820000   0.996703   1.000000
0.840000   0.996990   1.000000
0.860000   0.997993   1.000000
0.880000   0.998137   1.000000
0.900000   0.998280   1.000000
0.920000   0.998997   1.000000
0.940000   0.999140   1.000000
0.960000   0.999857   1.000000
0.980000   1.000000   1.000000
$$


$TABLE: Britton plot for twin law -h-2*l,-k,l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.005356   0.000000
0.019802   0.012115   0.008369
0.029703   0.020205   0.018048
0.039604   0.028848   0.027726
0.049505   0.037343   0.037404
0.059406   0.046873   0.047082
0.069307   0.056551   0.056760
0.079208   0.065600   0.066438
0.089109   0.074539   0.076116
0.099010   0.083737   0.085794
0.108911   0.093820   0.095472
0.118812   0.101762   0.105150
0.128713   0.111144   0.114828
0.138614   0.121745   0.124506
0.148515   0.131422   0.134185
0.158416   0.141506   0.143863
0.168317   0.152181   0.153541
0.178218   0.161748   0.163219
0.188119   0.170650   0.172897
0.198020   0.180180   0.182575
0.207921   0.189857   0.192253
0.217822   0.199645   0.201931
0.227723   0.209655   0.211609
0.237624   0.220182   0.221287
0.247525   0.230119   0.230965
0.257426   0.239907   0.240644
0.267327   0.249991   0.250322
0.277228   0.259816   0.260000
0.287129   0.269567   0.269678
0.297030   0.279725   0.279356
0.306931   0.289403   0.289034
0.316832   0.299597   0.298712
0.326733   0.309275   0.308390
0.336634   0.318361   0.318068
0.346535   0.328482   0.327746
0.356436   0.338308   0.337424
0.366337   0.347579   0.347102
0.376238   0.357109   0.356781
0.386139   0.365567   0.366459
0.396040   0.375319   0.376137
0.405941   0.385402   0.385815
0.415842   0.395745   0.395493
0.425743   0.405496   0.405171
0.435644   0.415248   0.414849
0.445545   0.425923   0.424527
0.455446   0.436228   0.434205
0.465347   0.445647   0.443883
0.475248   0.455915   0.453561
0.485149   0.465925   0.463240
$$


$TABLE: H test for possible twin law -h-2*l,-k,l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.030511   0.000000
0.020000   0.051049   0.020920
0.040000   0.071291   0.041839
0.060000   0.091090   0.062759
0.080000   0.109412   0.083678
0.100000   0.127142   0.104598
0.120000   0.150044   0.125517
0.140000   0.167627   0.146437
0.160000   0.185949   0.167356
0.180000   0.206339   0.188276
0.200000   0.227024   0.209195
0.220000   0.247710   0.230115
0.240000   0.264258   0.251034
0.260000   0.281989   0.271954
0.280000   0.299867   0.292874
0.300000   0.322030   0.313793
0.320000   0.343011   0.334713
0.340000   0.360298   0.355632
0.360000   0.379802   0.376552
0.380000   0.399453   0.397471
0.400000   0.419252   0.418391
0.420000   0.439495   0.439310
0.440000   0.460919   0.460230
0.460000   0.479093   0.481149
0.480000   0.502733   0.502069
0.500000   0.521203   0.522989
0.520000   0.541445   0.543908
0.540000   0.559840   0.564828
0.560000   0.577866   0.585747
0.580000   0.597370   0.606667
0.600000   0.615839   0.627586
0.620000   0.635638   0.648506
0.640000   0.654108   0.669425
0.660000   0.671838   0.690345
0.680000   0.691933   0.711264
0.700000   0.713061   0.732184
0.720000   0.733304   0.753103
0.740000   0.755024   0.774023
0.760000   0.775709   0.794943
0.780000   0.791519   0.815862
0.800000   0.811022   0.836782
0.820000   0.830822   0.857701
0.840000   0.851507   0.878621
0.860000   0.873522   0.899540
0.880000   0.894356   0.920460
0.900000   0.916519   0.941379
0.920000   0.936613   0.962299
0.940000   0.954344   0.983218
0.960000   0.973995   1.000000
0.980000   0.988918   1.000000
$$


$TABLE: Britton plot for twin law -h-2*l,k,h+l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.005413   0.000000
0.019802   0.012310   0.006519
0.029703   0.020059   0.016369
0.039604   0.029069   0.026219
0.049505   0.038265   0.036068
0.059406   0.047386   0.045918
0.069307   0.056804   0.055768
0.079208   0.065740   0.065618
0.089109   0.074861   0.075467
0.099010   0.083908   0.085317
0.108911   0.093400   0.095167
0.118812   0.102225   0.105017
0.128713   0.112347   0.114866
0.138614   0.122469   0.124716
0.148515   0.131887   0.134566
0.158416   0.141565   0.144416
0.168317   0.150760   0.154265
0.178218   0.160067   0.164115
0.188119   0.171709   0.173965
0.198020   0.181238   0.183815
0.207921   0.190174   0.193665
0.217822   0.199370   0.203514
0.227723   0.209270   0.213364
0.237624   0.220356   0.223214
0.247525   0.230552   0.233064
0.257426   0.239896   0.242913
0.267327   0.250167   0.252763
0.277228   0.260512   0.262613
0.287129   0.271116   0.272463
0.297030   0.281683   0.282312
0.306931   0.291324   0.292162
0.316832   0.300222   0.302012
0.326733   0.309974   0.311862
0.336634   0.318725   0.321711
0.346535   0.328624   0.331561
0.356436   0.338858   0.341411
0.366337   0.347979   0.351261
0.376238   0.359288   0.361110
0.386139   0.369373   0.370960
0.396040   0.380163   0.380810
0.405941   0.391101   0.390660
0.415842   0.401112   0.400509
0.425743   0.411605   0.410359
0.435644   0.422284   0.420209
0.445545   0.432406   0.430059
0.455446   0.444086   0.439909
0.465347   0.455951   0.449758
0.475248   0.468076   0.459608
0.485149   0.481201   0.469458
$$


$TABLE: H test for possible twin law -h-2*l,k,h+l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.000000   0.000000
0.020000   0.021802   0.020660
0.040000   0.049685   0.041321
0.060000   0.072525   0.061981
0.080000   0.098183   0.082642
0.100000   0.118650   0.103302
0.120000   0.143122   0.123963
0.140000   0.162403   0.144623
0.160000   0.183760   0.165284
0.180000   0.203930   0.185944
0.200000   0.224546   0.206605
0.220000   0.243678   0.227265
0.240000   0.265184   0.247926
0.260000   0.286392   0.268586
0.280000   0.306118   0.289247
0.300000   0.325695   0.309907
0.320000   0.346756   0.330568
0.340000   0.362922   0.351228
0.360000   0.381164   0.371889
0.380000   0.398072   0.392549
0.400000   0.416908   0.413209
0.420000   0.436930   0.433870
0.440000   0.459029   0.454530
0.460000   0.478309   0.475191
0.480000   0.500260   0.495851
0.500000   0.518799   0.516512
0.520000   0.537338   0.537172
0.540000   0.557953   0.557833
0.560000   0.577234   0.578493
0.580000   0.596811   0.599154
0.600000   0.614757   0.619814
0.620000   0.635373   0.640475
0.640000   0.654505   0.661135
0.660000   0.674379   0.681796
0.680000   0.694253   0.702456
0.700000   0.712940   0.723117
0.720000   0.733407   0.743777
0.740000   0.753875   0.764438
0.760000   0.775083   0.785098
0.780000   0.790656   0.805759
0.800000   0.808899   0.826419
0.820000   0.829218   0.847079
0.840000   0.850871   0.867740
0.860000   0.872228   0.888400
0.880000   0.894179   0.909061
0.900000   0.914498   0.929721
0.920000   0.935558   0.950382
0.940000   0.954245   0.971042
0.960000   0.973674   0.991703
0.980000   0.988283   1.000000
$$