#############################################################
##                        mmtbx.xtriage                    ##
##                                                         ##
##      P.H. Zwart, R.W. Grosse-Kunstleve & P.D. Adams     ##
##                                                         ##
#############################################################
Date 2006-03-28 Time 18:14:45 PST -0800


##-------------------------------------------##
## 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 = "p3.log"
  }
  xray_data {
    file_name = "aponat1_p3_scala1.mtz"
    obs_labels = MEAN
    calc_labels = None
    unit_cell = 42.03779984 42.03779984 149.1434021 90 90 120
    space_group = "P 3"
    high_resolution = None
    low_resolution = None
    low_resolution_for_twin_tests = 10
    high_resolution_for_twin_tests = None
    isigi_cut = 0
    minimum_bin_completenesss_enforcement = 0.75
    isigi_level_enforcement = 3
  }
  optional {
    hklout = None
    twinning {
      action = detwin *None
      twin_law = None
      fraction = None
    }
  }
}


Symmetry, cell and reflection file content summary

Miller array info: aponat1_p3_scala1.mtz:IMEAN_p3,SIGIMEAN_p3
Observation type: xray.amplitude
Type of data: double, size=7006
Type of sigmas: double, size=7006
Number of Miller indices: 7006
Anomalous flag: False
Unit cell: (42.0378, 42.0378, 149.143, 90, 90, 120)
Space group: P 3 (No. 143)
Systematic absences: 0
Centric reflections: 0
Resolution range: 36.4058 2.80033
Completeness in resolution range: 0.964881
Completeness with d_max=infinity: 0.96435

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


Matthews coefficient and Solvent content statistics

Number of residues unknown, assuming 50% solvent content

----------------------------------------------------------------
|              Best guess :  278  residues in the asu          |
----------------------------------------------------------------


Completeness and data strength analyses 

  The following table lists the completeness in various resolution
  ranges, after applying a I/sigI cut. Miller indices for which
  individual I/sigI values are larger than the value specified in
  the top row of the table, are retained, while other intensities
  are discarded. The resulting completeness profiles are an indication
  of the strength of the data.

----------------------------------------------------------------------------------------
| Res. Range   | I/sigI>1  | I/sigI>2  | I/sigI>3  | I/sigI>5  | I/sigI>10 | I/sigI>15 |
----------------------------------------------------------------------------------------
| 36.41 - 6.89 | 97.7%     | 97.3%     | 96.9%     | 96.7%     | 96.5%     | 95.3%     |
|  6.89 - 5.48 | 99.0%     | 99.0%     | 99.0%     | 98.4%     | 97.2%     | 97.0%     |
|  5.48 - 4.79 | 99.2%     | 99.2%     | 99.0%     | 98.8%     | 96.3%     | 95.7%     |
|  4.79 - 4.35 | 98.8%     | 98.6%     | 98.2%     | 97.4%     | 94.5%     | 92.3%     |
|  4.35 - 4.04 | 98.8%     | 97.6%     | 97.2%     | 95.6%     | 94.0%     | 91.7%     |
|  4.04 - 3.80 | 97.1%     | 95.8%     | 94.7%     | 93.5%     | 90.2%     | 84.2%     |
|  3.80 - 3.61 | 98.0%     | 96.9%     | 95.3%     | 90.4%     | 83.7%     | 76.8%     |
|  3.61 - 3.45 | 96.9%     | 94.8%     | 90.6%     | 86.8%     | 77.5%     | 69.3%     |
|  3.45 - 3.32 | 97.8%     | 96.5%     | 93.0%     | 89.0%     | 69.9%     | 58.1%     |
|  3.32 - 3.21 | 91.9%     | 88.7%     | 85.2%     | 77.3%     | 57.6%     | 43.7%     |
|  3.21 - 3.11 | 87.8%     | 82.0%     | 76.3%     | 64.5%     | 40.0%     | 27.8%     |
|  3.11 - 3.02 | 88.8%     | 80.3%     | 73.7%     | 59.6%     | 40.1%     | 25.9%     |
|  3.02 - 2.94 | 83.5%     | 73.4%     | 62.6%     | 49.6%     | 28.9%     | 14.9%     |
|  2.94 - 2.87 | 75.5%     | 61.9%     | 49.2%     | 34.3%     | 14.2%     | 6.9%      |
----------------------------------------------------------------------------------------

  The completeness of data for which I/sig(I)>3.00, exceeds  85% for
  for resolution ranges lower than 3.21A.
  The data is cut at this resolution for the potential twin tests 
  and intensity statistics.


Maximum likelihood isotropic Wilson scaling 
ML estimate of overall B value of aponat1_p3_scala1.mtz:IMEAN_p3,SIGIMEAN_p3:
89.45 A**(-2)
Estimated -log of scale factor of aponat1_p3_scala1.mtz:IMEAN_p3,SIGIMEAN_p3:
-2.23


Maximum likelihood anisotropic Wilson scaling 
ML estimate of overall B_cart value of aponat1_p3_scala1.mtz:IMEAN_p3,SIGIMEAN_p3:
98.85,  0.00,  0.00
       98.85,  0.00
              75.10
Equivalent representation as U_cif: 
 1.25,  0.63, -0.00
        1.25,  0.00
               0.95

ML estimate of  -log of scale factor of aponat1_p3_scala1.mtz:IMEAN_p3,SIGIMEAN_p3:
-2.23
Correcting for anisotropy in the data

Some basic intensity statistics follow.



Low resolution completeness analyses 

 The following table shows the completeness
 of the data to 5 Angstrom.
unused:         - 36.4067 [  0/4  ] 0.000
bin  1: 36.4067 - 10.6958 [127/131] 0.969
bin  2: 10.6958 -  8.5255 [130/130] 1.000
bin  3:  8.5255 -  7.4583 [129/130] 0.992
bin  4:  7.4583 -  6.7812 [132/132] 1.000
bin  5:  6.7812 -  6.2978 [132/134] 0.985
bin  6:  6.2978 -  5.9282 [112/113] 0.991
bin  7:  5.9282 -  5.6324 [133/135] 0.985
bin  8:  5.6324 -  5.3881 [131/131] 1.000
bin  9:  5.3881 -  5.1812 [116/117] 0.991
bin 10:  5.1812 -  5.0029 [143/145] 0.986
unused:  5.0029 -         [  0/0  ]



Mean intensity analyses 
 Analyses of the mean intensity. 
 Inspired by: Morris et al. (2004). J. Synch. Rad.11, 56-59.
 The following resolution shells are worrisome: 
------------------------------------------------
| d_spacing | z_score | compl. | <Iobs>/<Iexp> |
------------------------------------------------
|    5.411  |   4.89  |   0.99 |     0.701     |
------------------------------------------------

 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      : 1.56
      ( rms deviation   : 1.25 )
  mean bin completeness : 0.97
     ( rms deviation   : 0.04 )

 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  |   2.74  |   0.98 |     1.000     |
|    3.669  |   2.36  |   0.99 |     0.750     |
|    3.441  |   3.31  |   0.98 |     0.530     |
------------------------------------------------

 Abnormalities in mean intensity or completeness at
 resolution ranges with a relative ice ring intensity
 lower then 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 | Axis   | R metric (%) | delta (le Page) | delta (Lebedev) | Twin law  |
--------------------------------------------------------------------------------
|   M  | 2-fold | 0.000        | 0.000           | 0.000           | -h-k,k,-l |
|   M  | 2-fold | 0.000        | 0.000           | 0.000           | -h,-k,l   |
|   M  | 2-fold | 0.000        | 0.000           | 0.000           | h+k,-k,-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 : 6841

 Largest patterson peak with length larger then 15 Angstrom 

 Frac. coord.        :   0.327   -0.335    0.217
 Distance to origin  :  40.386
 Height (origin=100) :  10.510
 p_value(height)     :   1.323e-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  1.323e-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 then 1e-3 are a very strong indication for 
     the presence of translational pseudo symmetry.



Wilson ratio and moments 

Acentric reflections 
   <I^2>/<I>^2    :2.130   (untwinned: 2.000; perfect twin 1.500)
   <F>^2/<F^2>    :0.772   (untwinned: 0.785; perfect twin 0.885)
   <|E^2 - 1|>    :0.759   (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 |   0.101 |    0.095 |  0.000 |   0.248 |
| 0.2 |   0.195 |    0.181 |  0.000 |   0.345 |
| 0.3 |   0.274 |    0.259 |  0.000 |   0.419 |
| 0.4 |   0.348 |    0.330 |  0.000 |   0.474 |
| 0.5 |   0.407 |    0.394 |  0.000 |   0.520 |
| 0.6 |   0.467 |    0.451 |  0.000 |   0.561 |
| 0.7 |   0.519 |    0.503 |  0.000 |   0.597 |
| 0.8 |   0.568 |    0.551 |  0.000 |   0.629 |
| 0.9 |   0.609 |    0.593 |  0.000 |   0.657 |
| 1.0 |   0.642 |    0.632 |  0.000 |   0.683 |
-----------------------------------------------
| Maximum deviation acentric      :  0.018    |
| Maximum deviation centric       :  0.683    |
|                                             |
| <NZ(obs)-NZ(twinned)>_acentric  : +0.013    |
| <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|   :0.508  (untwinned: 0.500; perfect twin: 0.375)
  Mean  L^2  :0.343  (untwinned: 0.333; perfect twin: 0.200)

  The distribution of |L| values indicates a twin fraction of
  0.00. 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,k,-l
---------------------------------------------


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

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

mean |H| : 0.024   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.002   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.476
Estimation of twin fraction via cum. dist. of H: 0.480



Britton analyses

  Extrapolation performed on  0.47 < alpha < 0.495 
  Estimated twin fraction: 0.440
  Correlation: 0.9854

R vs R statistic:
  R_abs_twin = <|I1-I2|>/<|I1+I2|>
  Lebedev, Vagin, Murshudov. Acta Cryst. (2006). D62, 83-95

   R_abs_twin observed data   : 0.031

  R_sq_twin = <(I1-I2)^2>/<(I1+I2)^2>
   R_sq_twin observed data    : 0.001
  No calculated data available.
  R_twin for calculated data not determined.


---------------------------------------------
 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| : 0.463   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.309   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.037
Estimation of twin fraction via cum. dist. of H: 0.043



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: -0.004
  Correlation: 0.9997

R vs R statistic:
  R_abs_twin = <|I1-I2|>/<|I1+I2|>
  Lebedev, Vagin, Murshudov. Acta Cryst. (2006). D62, 83-95

   R_abs_twin observed data   : 0.472

  R_sq_twin = <(I1-I2)^2>/<(I1+I2)^2>
   R_sq_twin observed data    : 0.318
  No calculated data available.
  R_twin for calculated data not determined.


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


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

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

mean |H| : 0.461   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.309   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.039
Estimation of twin fraction via cum. dist. of H: 0.052



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: -0.005
  Correlation: 0.9996

R vs R statistic:
  R_abs_twin = <|I1-I2|>/<|I1+I2|>
  Lebedev, Vagin, Murshudov. Acta Cryst. (2006). D62, 83-95

   R_abs_twin observed data   : 0.510

  R_sq_twin = <(I1-I2)^2>/<(I1+I2)^2>
   R_sq_twin observed data    : 0.356
  No calculated data available.
  R_twin for calculated data not determined.



Exploring higher metric symmetry

Point group of data as discted by the space group is P 3
  the point group in the niggli setting is P 3
The point group of the lattice is P 6 2 2
A summary of R values for various possible point groups follow.

----------------------------------------------------------------------------------
| Point group | mean R_used | max R_used | mean R_unused | min R_unused | choice |
----------------------------------------------------------------------------------
| P 3         | None        | None       | 0.275         | 0.031        |        |
| P 6 2 2     | 0.275       | 0.510      | None          | None         |        |
| P 3 2 1     | 0.031       | 0.031      | 0.472         | 0.472        | <---   |
| P 6         | 0.472       | 0.472      | 0.031         | 0.031        |        |
| P 3 1 2     | 0.510       | 0.510      | 0.031         | 0.031        |        |
----------------------------------------------------------------------------------

R_used: mean and maximum R value for symmetry operators *used* in this point group
R_unused: mean and minimum R value for symmetry operators *not used* in this point group
 The likely point group of the data is:  P 3 2 1

Possible space groups in this point groups are:
   Unit cell: (42.0378, 42.0378, 149.143, 90, 90, 120)
   Space group: P 3 2 1 (No. 150)

   Unit cell: (42.0378, 42.0378, 149.143, 90, 90, 120)
   Space group: P 31 2 1 (No. 152)

   Unit cell: (42.0378, 42.0378, 149.143, 90, 90, 120)
   Space group: P 32 2 1 (No. 154)

Note that this analyses does not take into account the effects of twinning.
If the data is (allmost) perfectly twinned, the symmetry will appear to be
higher than it actually is.





-------------------------------------------------------------------------------
Twinning and intensity statistics summary (acentric data):

Statistics independent of twin laws
  - <I^2>/<I>^2 : 2.130
  - <F>^2/<F^2> : 0.772
  - <|E^2-1|>   : 0.759
  - 
, <L^2>: 0.508, 0.343
       Multivariate Z score L-test: 2.221 
       The multivariate Z score is a quality measure of the given
       spread in intensities. Good to reasonable data is expected
       to have a Z score lower than 3.5. 
       Large values can indicate twinning, but small values do not
       neccesarily exclude it. 


Statistics depending on twin laws
-------------------------------------------------------
| Operator  | type | R obs. | Britton alpha | H alpha |
-------------------------------------------------------
| -h-k,k,-l |   M  | 0.031  | 0.440         | 0.480   |
| -h,-k,l   |   M  | 0.472  | -0.004        | 0.043   |
| h+k,-k,-l |   M  | 0.510  | -0.005        | 0.052   |
-------------------------------------------------------

Patterson analyses
  - Largest peak height   : 10.510
   (correpsonding p value : 1.323e-01)


The largest off-origin peak in the Patterson function is 10.51% of the 
height of the origin peak. No significant pseudotranslation is detected.

The results of the L-test indicate that the intensity statistics
behave as expected. No twinning is suspected.
The symmetry of the lattice and intensity however suggests that the
input space group is too low. See the relevant sections of the log
file for more details on your choice of space groups.
As the symmetry is suspected to be incorrect, it is advicable to reconsider data processing.
 

-------------------------------------------------------------------------------


$TABLE: Intensity plots:
$GRAPHS
:Intensity plots 
:A:1,2,3,4:
$$
1/resol^2   <I>_smooth_approximation   <I>_via_binning   <I>_expected   $$ 
$$
0.010159   150302.223582   157446.139078   85266.049183
0.014159   105416.642637   99664.835486   66648.382854
0.018159   59362.797119   55952.329870   49077.829600
0.022159   37751.176767   39472.895721   42358.554575
0.026159   39059.831522   37857.798188   42515.691688
0.030159   40412.586904   41263.829714   46962.683931
0.034159   46810.678896   40152.495630   57241.057414
0.038159   67476.210580   74725.252368   73376.858266
0.042159   87505.595560   87689.209665   91425.309036
0.046159   96169.021791   90641.886221   106057.873076
0.050159   103818.611219   114637.537461   114104.869587
0.054159   117193.285739   108562.461099   115837.948989
0.058159   123662.058646   121298.806525   113806.017399
0.062159   112096.951314   116995.186249   110788.861109
0.066159   93546.866908   90479.462596   108362.743383
0.070159   87407.971763   90253.132867   106624.176796
0.074159   94685.686475   84201.143135   104770.663561
0.078159   99018.389386   120581.294477   101914.442079
0.082159   92299.023030   83763.677997   97639.046885
0.086159   84242.982086   76352.310293   92128.041399
0.090159   82452.134160   87615.223669   85964.254904
0.094159   79251.941465   78927.180431   79811.525242
0.098159   70017.317343   68422.765091   74162.833121
0.102159   66843.680250   64422.591418   69240.062379
0.106159   73526.644549   79765.585816   65033.211450
0.110159   72156.414271   66513.142512   61412.020184
0.114159   63492.302035   66202.751372   58237.197250
0.118159   61617.733593   57593.709163   55425.327343
0.122159   49755.313954   49603.532636   52957.743396
0.127521   56257.223098   55035.645591   50218.501734
$$


$TABLE: Z scores and completeness:
$GRAPHS
:Data sanity and completeness check 
:A:1,2,3:
$$
1/resol^2   Z_score   Completeness   $$ 
$$
0.010159   4.296319   1.000000
0.014159   3.318664   1.000000
0.018159   1.243812   0.991803
0.022159   0.845737   0.987261
0.026159   1.361004   0.993103
0.030159   1.595241   0.988024
0.034159   4.893041   0.994318
0.038159   0.236345   0.990050
0.042159   0.544233   0.994898
0.046159   2.086131   0.979275
0.050159   0.064271   0.995708
0.054159   0.870972   0.970443
0.058159   0.896311   1.000000
0.062159   0.813144   0.988462
0.066159   2.744572   0.977169
0.070159   2.762331   0.996212
0.074159   3.683245   0.988722
0.078159   2.359199   0.988048
0.082159   2.583508   0.989209
0.086159   3.313709   0.983051
0.090159   0.306173   0.982639
0.094159   0.178366   0.957597
0.098159   1.351389   0.955932
0.102159   1.252070   0.933535
0.106159   3.016989   0.943144
0.110159   1.278943   0.928571
0.114159   2.023772   0.940439
0.118159   0.652054   0.888579
0.122159   1.128001   0.902141
0.127521   1.267823   0.900000
$$


$TABLE: <I/sigma_I>:
$GRAPHS
:Signal to noise 
:N:1,2:
$$
1/resol^2   <I/sigma_I>;_Signal_to_noise   $$ 
$$
0.002754   47.695466
0.006754   61.288305
0.010754   63.775158
0.014754   67.173790
0.018754   69.664720
0.022754   63.462663
0.026754   64.413421
0.030754   60.795848
0.034754   60.376531
0.038754   59.632735
0.042754   59.100541
0.046754   59.391548
0.050754   53.108263
0.054754   55.289748
0.058754   50.583624
0.062754   45.627001
0.066754   40.933521
0.070754   35.303063
0.074754   30.320188
0.078754   32.325100
0.082754   22.803765
0.086754   19.449647
0.090754   17.839101
0.094754   16.400055
0.098754   12.781655
0.102754   11.795214
0.106754   11.344273
0.110754   8.929469
0.114754   7.593274
0.118754   6.026175
0.122754   4.482826
0.126754   4.881052
$$


$TABLE: NZ test:
$GRAPHS
:NZ test, acentric and centric data 
:A:1,2,3,4,5:
$$
z   Acentric_observed   Acentric_untwinned   Centric_observed   Centric_untwinned   $$ 
$$
0.000000   0.000000   0.000000   0.000000   0.000000
0.100000   0.101009   0.095200   0.000000   0.248100
0.200000   0.195439   0.181300   0.000000   0.345300
0.300000   0.274229   0.259200   0.000000   0.418700
0.400000   0.347902   0.329700   0.000000   0.473800
0.500000   0.406520   0.393500   0.000000   0.520500
0.600000   0.467183   0.451200   0.000000   0.561400
0.700000   0.518930   0.503400   0.000000   0.597200
0.800000   0.567607   0.550700   0.000000   0.628900
0.900000   0.608537   0.593400   0.000000   0.657200
1.000000   0.642450   0.632100   0.000000   0.683300
$$


$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   0.000757   0.000000   0.000000
0.020000   0.023291   0.020000   0.029996
0.040000   0.046014   0.040000   0.059968
0.060000   0.067411   0.060000   0.089892
0.080000   0.088809   0.080000   0.119744
0.100000   0.106230   0.100000   0.149500
0.120000   0.123840   0.120000   0.179136
0.140000   0.141072   0.140000   0.208628
0.160000   0.156599   0.160000   0.237952
0.180000   0.176292   0.180000   0.267084
0.200000   0.194849   0.200000   0.296000
0.220000   0.213217   0.220000   0.324676
0.240000   0.233289   0.240000   0.353088
0.260000   0.250142   0.260000   0.381212
0.280000   0.267752   0.280000   0.409024
0.300000   0.288960   0.300000   0.436500
0.320000   0.309222   0.320000   0.463616
0.340000   0.329294   0.340000   0.490348
0.360000   0.347661   0.360000   0.516672
0.380000   0.368680   0.380000   0.542564
0.400000   0.389888   0.400000   0.568000
0.420000   0.410339   0.420000   0.592956
0.440000   0.430222   0.440000   0.617408
0.460000   0.451051   0.460000   0.641332
0.480000   0.469419   0.480000   0.664704
0.500000   0.489680   0.500000   0.687500
0.520000   0.505965   0.520000   0.709696
0.540000   0.528688   0.540000   0.731268
0.560000   0.546866   0.560000   0.752192
0.580000   0.566559   0.580000   0.772444
0.600000   0.587957   0.600000   0.792000
0.620000   0.607839   0.620000   0.810836
0.640000   0.622988   0.640000   0.828928
0.660000   0.642681   0.660000   0.846252
0.680000   0.664268   0.680000   0.862784
0.700000   0.686423   0.700000   0.878500
0.720000   0.706684   0.720000   0.893376
0.740000   0.727514   0.740000   0.907388
0.760000   0.750994   0.760000   0.920512
0.780000   0.769173   0.780000   0.932724
0.800000   0.787919   0.800000   0.944000
0.820000   0.809316   0.820000   0.954316
0.840000   0.831282   0.840000   0.963648
0.860000   0.852111   0.860000   0.971972
0.880000   0.868396   0.880000   0.979264
0.900000   0.890172   0.900000   0.985500
0.920000   0.912327   0.920000   0.990656
0.940000   0.932589   0.940000   0.994708
0.960000   0.953418   0.960000   0.997632
0.980000   0.975194   0.980000   0.999404
$$


$TABLE: Britton plot for twin law -h-k,k,-l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.000593   0.000000
0.019802   0.000742   0.000000
0.029703   0.001483   0.000000
0.039604   0.001632   0.000000
0.049505   0.001780   0.000000
0.059406   0.001780   0.000000
0.069307   0.001780   0.000000
0.079208   0.002077   0.000000
0.089109   0.002522   0.000000
0.099010   0.003115   0.000000
0.108911   0.003560   0.000000
0.118812   0.003709   0.000000
0.128713   0.004005   0.000000
0.138614   0.004599   0.000000
0.148515   0.004895   0.000000
0.158416   0.005489   0.000000
0.168317   0.005785   0.000000
0.178218   0.005934   0.000000
0.188119   0.006379   0.000000
0.198020   0.006972   0.000000
0.207921   0.007269   0.000000
0.217822   0.008159   0.000000
0.227723   0.008752   0.000000
0.237624   0.010236   0.000000
0.247525   0.011126   0.000000
0.257426   0.011571   0.000000
0.267327   0.012016   0.000000
0.277228   0.013203   0.000000
0.287129   0.014686   0.000000
0.297030   0.015725   0.000000
0.306931   0.017060   0.000000
0.316832   0.018988   0.000000
0.326733   0.020323   0.000000
0.336634   0.021807   0.000000
0.346535   0.023439   0.000000
0.356436   0.025516   0.000000
0.366337   0.027444   0.000000
0.376238   0.030411   0.000000
0.386139   0.033971   0.000000
0.396040   0.037235   0.000000
0.405941   0.042279   0.000000
0.415842   0.048361   0.000000
0.425743   0.053553   0.000000
0.435644   0.060970   0.000000
0.445545   0.072690   0.021995
0.455446   0.083519   0.060568
0.465347   0.101914   0.099141
0.475248   0.130989   0.137714
0.485149   0.180240   0.176288
$$


$TABLE: H test for possible twin law -h-k,k,-l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.126706   0.000000
0.020000   0.644214   0.488293
0.040000   0.827596   0.976585
0.060000   0.902077   1.000000
0.080000   0.942433   1.000000
0.100000   0.960831   1.000000
0.120000   0.975074   1.000000
0.140000   0.980415   1.000000
0.160000   0.985163   1.000000
0.180000   0.989318   1.000000
0.200000   0.991691   1.000000
0.220000   0.993472   1.000000
0.240000   0.994065   1.000000
0.260000   0.995252   1.000000
0.280000   0.996439   1.000000
0.300000   0.997033   1.000000
0.320000   0.998220   1.000000
0.340000   0.998813   1.000000
0.360000   0.999407   1.000000
0.380000   1.000000   1.000000
0.400000   1.000000   1.000000
0.420000   1.000000   1.000000
0.440000   1.000000   1.000000
0.460000   1.000000   1.000000
0.480000   1.000000   1.000000
0.500000   1.000000   1.000000
0.520000   1.000000   1.000000
0.540000   1.000000   1.000000
0.560000   1.000000   1.000000
0.580000   1.000000   1.000000
0.600000   1.000000   1.000000
0.620000   1.000000   1.000000
0.640000   1.000000   1.000000
0.660000   1.000000   1.000000
0.680000   1.000000   1.000000
0.700000   1.000000   1.000000
0.720000   1.000000   1.000000
0.740000   1.000000   1.000000
0.760000   1.000000   1.000000
0.780000   1.000000   1.000000
0.800000   1.000000   1.000000
0.820000   1.000000   1.000000
0.840000   1.000000   1.000000
0.860000   1.000000   1.000000
0.880000   1.000000   1.000000
0.900000   1.000000   1.000000
0.920000   1.000000   1.000000
0.940000   1.000000   1.000000
0.960000   1.000000   1.000000
0.980000   1.000000   1.000000
$$


$TABLE: Britton plot for twin law -h,-k,l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.003512
0.009901   0.010404   0.012598
0.019802   0.019150   0.021685
0.029703   0.028498   0.030771
0.039604   0.036791   0.039858
0.049505   0.046441   0.048944
0.059406   0.055790   0.058031
0.069307   0.066194   0.067117
0.079208   0.075844   0.076204
0.089109   0.086248   0.085290
0.099010   0.094542   0.094377
0.108911   0.103589   0.103463
0.118812   0.112183   0.112550
0.128713   0.121381   0.121636
0.138614   0.128619   0.130723
0.148515   0.136460   0.139809
0.158416   0.147467   0.148896
0.168317   0.158172   0.157982
0.178218   0.166918   0.167069
0.188119   0.177021   0.176155
0.198020   0.188480   0.185242
0.207921   0.198130   0.194328
0.217822   0.209288   0.203415
0.227723   0.217883   0.212501
0.237624   0.226327   0.221588
0.247525   0.235676   0.230674
0.257426   0.244421   0.239761
0.267327   0.253468   0.248847
0.277228   0.263872   0.257934
0.287129   0.270959   0.267020
0.297030   0.277141   0.276107
0.306931   0.286641   0.285193
0.316832   0.295386   0.294280
0.326733   0.304735   0.303366
0.336634   0.314083   0.312453
0.346535   0.322226   0.321539
0.356436   0.331725   0.330625
0.366337   0.338812   0.339712
0.376238   0.347708   0.348798
0.386139   0.355097   0.357885
0.396040   0.361279   0.366971
0.405941   0.372738   0.376058
0.415842   0.381936   0.385144
0.425743   0.392039   0.394231
0.435644   0.401689   0.403317
0.445545   0.409379   0.412404
0.455446   0.416616   0.421490
0.465347   0.426417   0.430577
0.475248   0.437425   0.439663
0.485149   0.453257   0.448750
$$


$TABLE: H test for possible twin law -h,-k,l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.014475   0.000000
0.020000   0.079614   0.021880
0.040000   0.115199   0.043760
0.060000   0.139324   0.065639
0.080000   0.163450   0.087519
0.100000   0.181544   0.109399
0.120000   0.193607   0.131279
0.140000   0.205669   0.153158
0.160000   0.230398   0.175038
0.180000   0.248492   0.196918
0.200000   0.268999   0.218798
0.220000   0.281062   0.240678
0.240000   0.300965   0.262557
0.260000   0.315440   0.284437
0.280000   0.328709   0.306317
0.300000   0.348010   0.328197
0.320000   0.363088   0.350077
0.340000   0.382388   0.371956
0.360000   0.404101   0.393836
0.380000   0.424005   0.415716
0.400000   0.442099   0.437596
0.420000   0.454765   0.459475
0.440000   0.466828   0.481355
0.460000   0.489747   0.503235
0.480000   0.507238   0.525115
0.500000   0.528951   0.546995
0.520000   0.551870   0.568874
0.540000   0.572376   0.590754
0.560000   0.589867   0.612634
0.580000   0.607961   0.634514
0.600000   0.627865   0.656393
0.620000   0.648372   0.678273
0.640000   0.673703   0.700153
0.660000   0.687575   0.722033
0.680000   0.703257   0.743913
0.700000   0.729795   0.765792
0.720000   0.741858   0.787672
0.740000   0.758142   0.809552
0.760000   0.776840   0.831432
0.780000   0.799759   0.853311
0.800000   0.815440   0.875191
0.820000   0.828709   0.897071
0.840000   0.850422   0.918951
0.860000   0.871532   0.940831
0.880000   0.892039   0.962710
0.900000   0.910736   0.984590
0.920000   0.927021   1.000000
0.940000   0.942702   1.000000
0.960000   0.965018   1.000000
0.980000   0.983715   1.000000
$$


$TABLE: Britton plot for twin law h+k,-k,-l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.004914
0.009901   0.010241   0.013909
0.019802   0.019127   0.022904
0.029703   0.028916   0.031899
0.039604   0.036898   0.040893
0.049505   0.046687   0.049888
0.059406   0.056777   0.058883
0.069307   0.066416   0.067878
0.079208   0.077259   0.076873
0.089109   0.086145   0.085867
0.099010   0.095331   0.094862
0.108911   0.103765   0.103857
0.118812   0.112500   0.112852
0.128713   0.120783   0.121846
0.138614   0.129367   0.130841
0.148515   0.137801   0.139836
0.158416   0.148645   0.148831
0.168317   0.158584   0.157825
0.178218   0.167771   0.166820
0.188119   0.178464   0.175815
0.198020   0.188253   0.184810
0.207921   0.197590   0.193804
0.217822   0.207078   0.202799
0.227723   0.216717   0.211794
0.237624   0.225904   0.220789
0.247525   0.234940   0.229784
0.257426   0.243072   0.238778
0.267327   0.253916   0.247773
0.277228   0.263253   0.256768
0.287129   0.270934   0.265763
0.297030   0.276054   0.274757
0.306931   0.284488   0.283752
0.316832   0.293373   0.292747
0.326733   0.303313   0.301742
0.336634   0.311747   0.310736
0.346535   0.321235   0.319731
0.356436   0.329669   0.328726
0.366337   0.337349   0.337721
0.376238   0.348193   0.346715
0.386139   0.354217   0.355710
0.396040   0.361596   0.364705
0.405941   0.371386   0.373700
0.415842   0.380873   0.382695
0.425743   0.391566   0.391689
0.435644   0.401205   0.400684
0.445545   0.408434   0.409679
0.455446   0.415211   0.418674
0.465347   0.421687   0.427668
0.475248   0.430723   0.436663
0.485149   0.438855   0.445658
$$


$TABLE: H test for possible twin law h+k,-k,-l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.085241   0.000000
0.020000   0.115361   0.022319
0.040000   0.131627   0.044638
0.060000   0.150301   0.066957
0.080000   0.165964   0.089275
0.100000   0.184036   0.111594
0.120000   0.191265   0.133913
0.140000   0.209639   0.156232
0.160000   0.231325   0.178551
0.180000   0.250000   0.200870
0.200000   0.266265   0.223188
0.220000   0.286145   0.245507
0.240000   0.297590   0.267826
0.260000   0.315663   0.290145
0.280000   0.331325   0.312464
0.300000   0.343976   0.334783
0.320000   0.363855   0.357101
0.340000   0.383735   0.379420
0.360000   0.408434   0.401739
0.380000   0.426506   0.424058
0.400000   0.442169   0.446377
0.420000   0.456024   0.468696
0.440000   0.464458   0.491014
0.460000   0.489157   0.513333
0.480000   0.509036   0.535652
0.500000   0.531325   0.557971
0.520000   0.555422   0.580290
0.540000   0.571084   0.602609
0.560000   0.589157   0.624928
0.580000   0.607831   0.647246
0.600000   0.627711   0.669565
0.620000   0.648193   0.691884
0.640000   0.674096   0.714203
0.660000   0.687349   0.736522
0.680000   0.708434   0.758841
0.700000   0.727108   0.781159
0.720000   0.741566   0.803478
0.740000   0.760843   0.825797
0.760000   0.777711   0.848116
0.780000   0.798795   0.870435
0.800000   0.814458   0.892754
0.820000   0.831325   0.915072
0.840000   0.850000   0.937391
0.860000   0.874699   0.959710
0.880000   0.889759   0.982029
0.900000   0.910843   1.000000
0.920000   0.928313   1.000000
0.940000   0.943373   1.000000
0.960000   0.965663   1.000000
0.980000   0.983735   1.000000
$$