#############################################################
##                        mmtbx.xtriage                    ##
##                                                         ##
##      P.H. Zwart, R.W. Grosse-Kunstleve & P.D. Adams     ##
##                                                         ##
#############################################################
Date 2006-03-28 Time 18:14:31 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 = "p321.log"
  }
  xray_data {
    file_name = "aponat1_p321_scala1.mtz"
    obs_labels = MEAN
    calc_labels = None
    unit_cell = 42.03779984 42.03779984 149.1434021 90 90 120
    space_group = "P 3 2 1"
    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_p321_scala1.mtz:IMEAN_p321,SIGIMEAN_p321
Observation type: xray.amplitude
Type of data: double, size=4014
Type of sigmas: double, size=4014
Number of Miller indices: 4014
Anomalous flag: False
Unit cell: (42.0378, 42.0378, 149.143, 90, 90, 120)
Space group: P 3 2 1 (No. 150)
Systematic absences: 0
Centric reflections: 988
Resolution range: 36.4058 2.80033
Completeness in resolution range: 0.962128
Completeness with d_max=infinity: 0.961207

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


Matthews coefficient and Solvent content statistics

Number of residues unknown, assuming 50% solvent content

----------------------------------------------------------------
|              Best guess :  139  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 | 96.7%     | 96.1%     | 95.2%     | 95.2%     | 94.6%     | 93.7%     |
|  6.89 - 5.48 | 98.3%     | 98.3%     | 98.3%     | 97.3%     | 95.9%     | 95.3%     |
|  5.48 - 4.79 | 99.0%     | 99.0%     | 98.6%     | 97.9%     | 96.2%     | 94.8%     |
|  4.79 - 4.35 | 97.9%     | 97.6%     | 96.9%     | 96.2%     | 93.7%     | 91.3%     |
|  4.35 - 4.04 | 98.2%     | 96.4%     | 96.1%     | 94.7%     | 92.5%     | 90.4%     |
|  4.04 - 3.80 | 96.5%     | 94.6%     | 93.1%     | 91.9%     | 89.2%     | 85.8%     |
|  3.80 - 3.61 | 98.3%     | 96.9%     | 95.1%     | 92.3%     | 84.3%     | 80.1%     |
|  3.61 - 3.45 | 97.1%     | 95.2%     | 90.8%     | 87.1%     | 79.0%     | 72.4%     |
|  3.45 - 3.32 | 97.4%     | 95.9%     | 94.8%     | 89.5%     | 76.0%     | 64.4%     |
|  3.32 - 3.21 | 90.7%     | 87.7%     | 85.1%     | 78.7%     | 63.1%     | 51.5%     |
|  3.21 - 3.11 | 89.3%     | 82.9%     | 78.3%     | 68.7%     | 47.7%     | 33.8%     |
|  3.11 - 3.02 | 89.4%     | 83.1%     | 77.6%     | 66.9%     | 46.1%     | 33.5%     |
|  3.02 - 2.94 | 86.4%     | 74.5%     | 67.5%     | 55.6%     | 35.7%     | 22.7%     |
|  2.94 - 2.87 | 77.1%     | 63.0%     | 56.1%     | 40.8%     | 21.8%     | 10.3%     |
----------------------------------------------------------------------------------------

  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_p321_scala1.mtz:IMEAN_p321,SIGIMEAN_p321:
92.64 A**(-2)
Estimated -log of scale factor of aponat1_p321_scala1.mtz:IMEAN_p321,SIGIMEAN_p321:
-2.15


Maximum likelihood anisotropic Wilson scaling 
ML estimate of overall B_cart value of aponat1_p321_scala1.mtz:IMEAN_p321,SIGIMEAN_p321:
104.03,  0.00,  0.00
      104.03,  0.00
              74.01
Equivalent representation as U_cif: 
 1.32,  0.66, -0.00
        1.32,  0.00
               0.94

ML estimate of  -log of scale factor of aponat1_p321_scala1.mtz:IMEAN_p321,SIGIMEAN_p321:
-2.15
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 [97/102] 0.951
bin  2: 10.6958 -  8.5255 [88/88 ] 1.000
bin  3:  8.5255 -  7.4583 [78/79 ] 0.987
bin  4:  7.4583 -  6.7812 [86/86 ] 1.000
bin  5:  6.7812 -  6.2978 [78/80 ] 0.975
bin  6:  6.2978 -  5.9282 [70/71 ] 0.986
bin  7:  5.9282 -  5.6324 [79/81 ] 0.975
bin  8:  5.6324 -  5.3881 [76/76 ] 1.000
bin  9:  5.3881 -  5.1812 [70/71 ] 0.986
bin 10:  5.1812 -  5.0029 [85/86 ] 0.988
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  |   6.55  |   0.99 |     0.577     |
|    3.888  |   4.72  |   0.97 |     0.693     |
|    3.672  |   5.16  |   0.99 |     0.691     |
------------------------------------------------

 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      : 2.07
      ( rms deviation   : 1.41 )
  mean bin completeness : 0.96
     ( rms deviation   : 0.03 )

 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  |   4.72  |   0.97 |     1.000     |
|    3.669  |   0.19  |   0.99 |     0.750     |
|    3.441  |   3.99  |   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,l  |
-------------------------------------------------------------------------------
M:  Merohedral twin law
PM: Pseudomerohedral twin law

  1 merohedral twin operators found
  0 pseudo-merohedral twin operators found
In total,   1 twin operator were found


Number of centrics  : 912
Number of acentrics : 2981

 Largest patterson peak with length larger then 15 Angstrom 

 Frac. coord.        :   0.327   -0.336    0.217
 Distance to origin  :  40.392
 Height (origin=100) :  10.491
 p_value(height)     :   1.332e-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  1.332e-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    :2.058   (untwinned: 2.000; perfect twin 1.500)
   <F>^2/<F^2>    :0.784   (untwinned: 0.785; perfect twin 0.885)
   <|E^2 - 1|>    :0.731   (untwinned: 0.736; perfect twin 0.541)


Centric reflections 
   <I^2>/<I>^2    :2.582   (untwinned: 3.000; perfect twin 2.000)
   <F>^2/<F^2>    :0.685   (untwinned: 0.637; perfect twin 0.785)
   <|E^2 - 1|>    :0.930   (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 |   0.093 |    0.095 |  0.190 |   0.248 |
| 0.2 |   0.184 |    0.181 |  0.293 |   0.345 |
| 0.3 |   0.265 |    0.259 |  0.360 |   0.419 |
| 0.4 |   0.339 |    0.330 |  0.411 |   0.474 |
| 0.5 |   0.401 |    0.394 |  0.470 |   0.520 |
| 0.6 |   0.461 |    0.451 |  0.519 |   0.561 |
| 0.7 |   0.517 |    0.503 |  0.559 |   0.597 |
| 0.8 |   0.566 |    0.551 |  0.598 |   0.629 |
| 0.9 |   0.606 |    0.593 |  0.628 |   0.657 |
| 1.0 |   0.642 |    0.632 |  0.651 |   0.683 |
-----------------------------------------------
| Maximum deviation acentric      :  0.015    |
| Maximum deviation centric       :  0.063    |
|                                             |
| <NZ(obs)-NZ(twinned)>_acentric  : +0.008    |
| <NZ(obs)-NZ(twinned)>_centric   : -0.041    |
-----------------------------------------------


 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|   :0.483  (untwinned: 0.500; perfect twin: 0.375)
  Mean  L^2  :0.313  (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,l
---------------------------------------------


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

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

mean |H| : 0.445   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.293   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.055
Estimation of twin fraction via cum. dist. of H: 0.063



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: 0.001
  Correlation: 0.9998

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   : 0.526

  R_sq_twin = <(I1-I2)^2>/<(I1+I2)^2>
   R_sq_twin observed data    : 0.365
  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 2 1
  the point group in the niggli setting is P 3 2 1
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 6 2 2     | 0.526       | 0.526      | None          | None         |        |
| P 3 2 1     | None        | None       | 0.526         | 0.526        | <---   |
----------------------------------------------------------------------------------

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 : 2.058
  - <F>^2/<F^2> : 0.784
  - <|E^2-1|>   : 0.731
  - 
, <L^2>: 0.483, 0.313
       Multivariate Z score L-test: 1.827 
       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,l  |   M  | 0.526  | 0.001         | 0.063   |
------------------------------------------------------

Patterson analyses
  - Largest peak height   : 10.491
   (correpsonding p value : 1.332e-01)


The largest off-origin peak in the Patterson function is 10.49% 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.
Even though no twinning is suspected, it might be worthwhile carrying out 
a refinement using a dedicated twin target anyway, as twinned structures with
low twin fractions are difficult to distinguish from non-twinned structures.


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


$TABLE: Intensity plots:
$GRAPHS
:Intensity plots 
:A:1,2,3,4:
$$
1/resol^2   <I>_smooth_approximation   <I>_via_binning   <I>_expected   $$ 
$$
0.010159   102589.563630   113929.939917   85266.049183
0.014159   78213.676029   77997.418743   66648.382854
0.018159   49557.768569   43228.792644   49077.829600
0.022159   32974.975076   33038.397430   42358.554575
0.026159   32514.387198   30225.338873   42515.691688
0.030159   33275.840906   34249.187407   46962.683931
0.034159   39669.049724   33031.101750   57241.057414
0.038159   56855.818871   61441.971197   73376.858266
0.042159   72899.428523   74726.245187   91425.309036
0.046159   80172.063225   76675.955986   106057.873076
0.050159   86531.325535   92548.058470   114104.869587
0.054159   97276.971980   90621.708552   115837.948989
0.058159   103663.769600   104437.089217   113806.017399
0.062159   97041.453822   104038.211348   110788.861109
0.066159   83813.584355   75108.703258   108362.743383
0.070159   77449.625652   81669.819122   106624.176796
0.074159   80575.495491   72368.570424   104770.663561
0.078159   83847.368155   100279.236917   101914.442079
0.082159   81221.856948   76961.705392   97639.046885
0.086159   76849.202635   69227.595593   92128.041399
0.090159   74426.927845   78528.751350   85964.254904
0.094159   70035.528767   70129.533818   79811.525242
0.098159   62720.330823   59678.949405   74162.833121
0.102159   60950.955887   58286.538560   69240.062379
0.106159   66044.771616   73024.261016   65033.211450
0.110159   65231.166509   61270.994018   61412.020184
0.114159   58643.925842   60627.435668   58237.197250
0.118159   55866.829376   52541.563618   55425.327343
0.122159   47939.300668   46608.001907   52957.743396
0.127521   51020.747905   51052.037430   50218.501734
$$


$TABLE: Z scores and completeness:
$GRAPHS
:Data sanity and completeness check 
:A:1,2,3:
$$
1/resol^2   Z_score   Completeness   $$ 
$$
0.010159   1.868577   1.000000
0.014159   1.180944   1.000000
0.018159   1.093094   0.987342
0.022159   2.540960   0.978723
0.026159   3.544265   0.988889
0.030159   3.377053   0.980392
0.034159   6.545405   0.990291
0.038159   1.983279   0.991667
0.042159   2.209714   0.991228
0.046159   3.600283   0.963636
0.050159   2.504095   0.992806
0.054159   2.774095   0.957627
0.058159   0.986120   1.000000
0.062159   0.761306   0.980000
0.066159   4.717181   0.968750
0.070159   3.523743   0.993151
0.074159   5.163427   0.993333
0.078159   0.189707   0.986207
0.082159   3.198489   0.980892
0.086159   3.992849   0.981366
0.090159   1.171936   0.975758
0.094159   1.656419   0.949686
0.098159   2.939991   0.951220
0.102159   2.363658   0.944134
0.106159   1.333515   0.939024
0.110159   0.029282   0.928962
0.114159   0.499565   0.943503
0.118159   0.709373   0.878788
0.122159   1.676926   0.887006
0.127521   0.178618   0.924242
$$


$TABLE: <I/sigma_I>:
$GRAPHS
:Signal to noise 
:N:1,2:
$$
1/resol^2   <I/sigma_I>;_Signal_to_noise   $$ 
$$
0.002754   47.901015
0.006754   68.294206
0.010754   73.109233
0.014754   78.115963
0.018754   79.032166
0.022754   76.672106
0.026754   76.107420
0.030754   74.040731
0.034754   73.529084
0.038754   71.022757
0.042754   73.260936
0.046754   73.856620
0.050754   63.958712
0.054754   68.226033
0.058754   63.311262
0.062754   55.744074
0.066754   49.890641
0.070754   44.631636
0.074754   37.370935
0.078754   39.759392
0.082754   28.984308
0.086754   24.714502
0.090754   21.751331
0.094754   20.439621
0.098754   16.136174
0.102754   14.642566
0.106754   14.304292
0.110754   11.020785
0.114754   9.606846
0.118754   7.589231
0.122754   5.665867
0.126754   6.033919
$$


$TABLE: NZ test:
$GRAPHS
:NZ test, acentric and centric data 
:A:1,2,3,4,5:
$$
z   Acentric_observed   Acentric_untwinned   Centric_observed   Centric_untwinned   $$ 
$$
0.000000   0.000000   0.000000   0.000000   0.000000
0.100000   0.092922   0.095200   0.189693   0.248100
0.200000   0.183831   0.181300   0.292763   0.345300
0.300000   0.265347   0.259200   0.359649   0.418700
0.400000   0.339483   0.329700   0.411184   0.473800
0.500000   0.400537   0.393500   0.470395   0.520500
0.600000   0.460584   0.451200   0.518640   0.561400
0.700000   0.517276   0.503400   0.559211   0.597200
0.800000   0.565582   0.550700   0.597588   0.628900
0.900000   0.606172   0.593400   0.628289   0.657200
1.000000   0.641731   0.632100   0.651316   0.683300
$$


$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   0.009843   0.000000   0.000000
0.020000   0.025098   0.020000   0.029996
0.040000   0.045276   0.040000   0.059968
0.060000   0.062992   0.060000   0.089892
0.080000   0.079724   0.080000   0.119744
0.100000   0.097933   0.100000   0.149500
0.120000   0.118110   0.120000   0.179136
0.140000   0.138780   0.140000   0.208628
0.160000   0.160925   0.160000   0.237952
0.180000   0.181102   0.180000   0.267084
0.200000   0.203248   0.200000   0.296000
0.220000   0.221949   0.220000   0.324676
0.240000   0.244094   0.240000   0.353088
0.260000   0.268701   0.260000   0.381212
0.280000   0.291339   0.280000   0.409024
0.300000   0.312008   0.300000   0.436500
0.320000   0.332677   0.320000   0.463616
0.340000   0.354823   0.340000   0.490348
0.360000   0.379921   0.360000   0.516672
0.380000   0.396161   0.380000   0.542564
0.400000   0.417323   0.400000   0.568000
0.420000   0.440945   0.420000   0.592956
0.440000   0.464075   0.440000   0.617408
0.460000   0.485728   0.460000   0.641332
0.480000   0.507382   0.480000   0.664704
0.500000   0.528051   0.500000   0.687500
0.520000   0.544783   0.520000   0.709696
0.540000   0.564961   0.540000   0.731268
0.560000   0.584154   0.560000   0.752192
0.580000   0.610236   0.580000   0.772444
0.600000   0.636319   0.600000   0.792000
0.620000   0.655512   0.620000   0.810836
0.640000   0.671752   0.640000   0.828928
0.660000   0.687992   0.660000   0.846252
0.680000   0.709154   0.680000   0.862784
0.700000   0.732776   0.700000   0.878500
0.720000   0.750492   0.720000   0.893376
0.740000   0.768701   0.740000   0.907388
0.760000   0.790846   0.760000   0.920512
0.780000   0.809055   0.780000   0.932724
0.800000   0.825787   0.800000   0.944000
0.820000   0.841535   0.820000   0.954316
0.840000   0.859744   0.840000   0.963648
0.860000   0.877461   0.860000   0.971972
0.880000   0.894193   0.880000   0.979264
0.900000   0.915354   0.900000   0.985500
0.920000   0.936024   0.920000   0.990656
0.940000   0.948819   0.940000   0.994708
0.960000   0.969488   0.960000   0.997632
0.980000   0.985236   0.980000   0.999404
$$


$TABLE: Britton plot for twin law -h,-k,l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.005818   0.007610
0.019802   0.015058   0.016527
0.029703   0.024298   0.025445
0.039604   0.030801   0.034363
0.049505   0.042437   0.043281
0.059406   0.052704   0.052199
0.069307   0.062628   0.061117
0.079208   0.070157   0.070035
0.089109   0.078713   0.078953
0.099010   0.090349   0.087871
0.108911   0.096851   0.096788
0.118812   0.104723   0.105706
0.128713   0.113621   0.114624
0.138614   0.121834   0.123542
0.148515   0.128337   0.132460
0.158416   0.139288   0.141378
0.168317   0.149213   0.150296
0.178218   0.158795   0.159214
0.188119   0.168720   0.168132
0.198020   0.177618   0.177050
0.207921   0.188569   0.185967
0.217822   0.196099   0.194885
0.227723   0.205339   0.203803
0.237624   0.214579   0.212721
0.247525   0.224504   0.221639
0.257426   0.234771   0.230557
0.267327   0.244695   0.239475
0.277228   0.250856   0.248393
0.287129   0.260096   0.257311
0.297030   0.265229   0.266228
0.306931   0.274812   0.275146
0.316832   0.284052   0.284064
0.326733   0.295003   0.292982
0.336634   0.302190   0.301900
0.346535   0.311773   0.310818
0.356436   0.318617   0.319736
0.366337   0.327515   0.328654
0.376238   0.335387   0.337572
0.386139   0.343258   0.346489
0.396040   0.352498   0.355407
0.405941   0.362081   0.364325
0.415842   0.373717   0.373243
0.425743   0.384668   0.382161
0.435644   0.395277   0.391079
0.445545   0.401437   0.399997
0.455446   0.407598   0.408915
0.465347   0.416153   0.417833
0.475248   0.424709   0.426750
0.485149   0.431554   0.435668
$$


$TABLE: H test for possible twin law -h,-k,l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.101985   0.000000
0.020000   0.115674   0.022880
0.040000   0.138946   0.045760
0.060000   0.152635   0.068640
0.080000   0.171800   0.091520
0.100000   0.185489   0.114400
0.120000   0.199179   0.137280
0.140000   0.218344   0.160160
0.160000   0.237509   0.183040
0.180000   0.263518   0.205920
0.200000   0.279945   0.228800
0.220000   0.299110   0.251680
0.240000   0.315537   0.274560
0.260000   0.336071   0.297440
0.280000   0.352498   0.320320
0.300000   0.366188   0.343200
0.320000   0.386721   0.366080
0.340000   0.401780   0.388960
0.360000   0.433265   0.411840
0.380000   0.448323   0.434720
0.400000   0.466119   0.457600
0.420000   0.478439   0.480480
0.440000   0.490760   0.503360
0.460000   0.508556   0.526240
0.480000   0.527721   0.549120
0.500000   0.556468   0.572000
0.520000   0.579740   0.594880
0.540000   0.598905   0.617760
0.560000   0.612594   0.640640
0.580000   0.629021   0.663520
0.600000   0.649555   0.686400
0.620000   0.671458   0.709280
0.640000   0.690623   0.732160
0.660000   0.701574   0.755040
0.680000   0.722108   0.777920
0.700000   0.745380   0.800800
0.720000   0.761807   0.823680
0.740000   0.780972   0.846560
0.760000   0.798768   0.869440
0.780000   0.817933   0.892320
0.800000   0.826146   0.915200
0.820000   0.849418   0.938080
0.840000   0.871321   0.960960
0.860000   0.883641   0.983840
0.880000   0.900068   1.000000
0.900000   0.915127   1.000000
0.920000   0.938398   1.000000
0.940000   0.950719   1.000000
0.960000   0.969884   1.000000
0.980000   0.991786   1.000000
$$