MATLAB Examples

Contents

ellipseFit4HC_EXAMPLE

(c) Viktor Witkovsky (witkovsky@savba.sk) Ver.: 31-Jul-2014 18:27:32

clear

GENERATE the uncorrelated measurements: x and y

Feel free to experiment with the setting parameters
alpha0true = 0;                             % x-center (offset x)
beta0true  = 0;                             % y-center (offset x)
alpha1true = 1;                             % x-amplitude
beta1true  = 1;                             % y-amplitude
phi0true   = 0;                             % phase offset

sigma = 0.001;                          % std of x and y independent errors
n = 500;                               % number of measurements points
cycles = 1;                             % measurement interval,  # cycles
phitrue = cycles*(2*pi)*sort(rand(n,1));    % true phases phi_i

% true values:  X and Y
Xmean = @(t) alpha0true + alpha1true * cos(t);
Ymean = @(t) beta0true + beta1true * sin(t + phi0true);

% measurements:  X + error, Y + error,
x = Xmean(phitrue) + sigma * randn(size(phitrue));
y = Ymean(phitrue) + sigma * randn(size(phitrue));

Fit the ellipse based on measured data

options.alpha = 0.05;
options.correlation = 0;
options.displconst = 633.3/(4*pi);
options.displunit = 'nanometer [nm]';
result = ellipseFit4HC(x,y,options);

disp(result)
  -------------------------------------------------
  ESTIMATED ELLIPSE PARAMETERS                     
  X^2 + B*Y^2 + C*X*Y + D*X + F*Y + G = 0          
  -------------------------------------------------
          ESTIMATE         STD        DF     FACTOR       LOWER         UPPER   
         ___________    __________    ___    ______    ___________    __________

    B         1.0001     0.0002517    495    1.9648        0.99956        1.0005
    C    -7.2954e-05    0.00025273    495    1.9648     -0.0005695     0.0004236
    D    -5.1167e-06    0.00012533    495    1.9648    -0.00025136    0.00024113
    F    -8.4915e-05    0.00012687    495    1.9648    -0.00033418    0.00016435
    G             -1    0.00015294    495    1.9648        -1.0003      -0.99973

  -------------------------------------------------
  ESTIMATED ELLIPSE PARAMETERS                     
  X(phi) = alpha_0 + alpha_1 * cos(phi)            
  Y(phi) = beta_0  + beta_1  * sin(phi + phi_0     
  -------------------------------------------------
                ESTIMATE        STD        DF     FACTOR       LOWER   
               __________    __________    ___    ______    ___________

    alpha_0    2.5599e-06    6.2665e-05    495    1.9648    -0.00012056
    beta_0     4.2455e-05     6.343e-05    495    1.9648    -8.2169e-05
    alpha_1             1    7.6468e-05    495    1.9648        0.99987
    beta_1        0.99999    7.7723e-05    495    1.9648        0.99984
    phi_0      3.6476e-05    0.00012584    495    1.9648    -0.00021078


                 UPPER   
               __________

    alpha_0    0.00012568
    beta_0     0.00016708
    alpha_1        1.0002
    beta_1         1.0001
    phi_0      0.00028373

                  Description: 'Ellipse Fit by Iterated Locally Best Linea...'
           ABCDEF_Description: 'A*x^2 + 2*B*x*y + C*y^2 + 2*D*x + 2*E*y + ...'
                 ABCDEF_Names: {'A'  'B'  'C'  'D'  'E'  'F'}
                   ABCDEF_fit: [1x6 double]
                   ABCDEF_std: [1x6 double]
            BCDFG_Description: 'x^2 + B*y^2 +  C*x*y + D*x + F*y + G = 0'
                  BCDFG_Names: {'B'  'C'  'D'  'F'  'G'}
                    BCDFG_fit: [1x5 double]
                    BCDFG_std: [1x5 double]
                    BCDFG_cov: [5x5 double]
    EllipsePars_Description_X: 'X(phi) = alpha_0 + alpha_1 * cos(phi)'
    EllipsePars_Description_Y: 'Y(phi) = beta_0  + beta_1  * sin(phi + phi_0)'
            EllipsePars_Names: {1x5 cell}
              EllipsePars_fit: [1x5 double]
              EllipsePars_std: [1x5 double]
                     mu_X_fit: [500x1 double]
                     mu_X_std: [500x1 double]
                     nu_Y_fit: [500x1 double]
                     nu_Y_std: [500x1 double]
                     X_fitfun: @(t)alpha0_fit+alpha1_fit*cos(t)
                     Y_fitfun: @(t)beta0_fit+beta1_fit*sin(t+phi0_fit)
                    x_res_fit: [500x1 double]
                    x_res_std: [500x1 double]
                    y_res_fit: [500x1 double]
                    y_res_std: [500x1 double]
                    sigma_fit: 9.9570e-04
                   sigma2_fit: 9.9141e-07
                      phi_fit: [500x1 double]
                      phi_std: [500x1 double]
                  phi_std_max: 0.0010
                  phi_std_min: 9.9765e-04
     Displacement_Description: 'Displacement_fit = Displacement_const * ph...'
             Displacement_fit: [500x1 double]
             Displacement_std: [500x1 double]
         Displacement_std_max: 0.0507
         Displacement_std_min: 0.0503
           Displacement_const: 50.3964
            Displacement_unit: 'nanometer [nm]'
                  TABLE_BCDFG: [5x6 table]
            TABLE_EllipsePars: [5x6 table]
          TABLE_Displacements: [500x7 table]
                       x_data: [500x1 double]
                       y_data: [500x1 double]
          used_Correlation_XY: 0
                      options: [1x1 struct]
                    criterion: 7.6311e-13
                        loops: 4
                       tictoc: 0.0132

Display statistics of the fitted displacements (!! Table with n rows !!)

TABLE1 = result.TABLE_EllipsePars;
TABLE2 = result.TABLE_Displacements;

disp(TABLE2)
disp(['Displacement unit: ' result.Displacement_unit])
    OBSERVATION    ESTIMATE      STD       DF     FACTOR      LOWER  
    ___________    ________    ________    ___    ______    _________

      1            0.066443    0.050673    495    1.9648    -0.033118
      2             0.27813    0.050673    495    1.9648      0.17857
      3             0.73274    0.050673    495    1.9648      0.63318
      4              1.1799    0.050672    495    1.9648       1.0803
      5               1.258    0.050672    495    1.9648       1.1584
      6              1.3765    0.050672    495    1.9648        1.277
      7              1.9412    0.050671    495    1.9648       1.8417
      8              2.7539     0.05067    495    1.9648       2.6544
      9              3.5033    0.050668    495    1.9648       3.4037
     10                 4.3    0.050667    495    1.9648       4.2005
     11               4.609    0.050666    495    1.9648       4.5094
     12              5.2952    0.050665    495    1.9648       5.1956
     13              5.3387    0.050665    495    1.9648       5.2391
     14              5.3537    0.050664    495    1.9648       5.2542
     15               5.729    0.050664    495    1.9648       5.6294
     16               5.681    0.050664    495    1.9648       5.5814
     17              7.0522     0.05066    495    1.9648       6.9527
     18              7.0983     0.05066    495    1.9648       6.9987
     19               7.171     0.05066    495    1.9648       7.0714
     20              8.5729    0.050655    495    1.9648       8.4734
     21              9.9495     0.05065    495    1.9648         9.85
     22              11.529    0.050644    495    1.9648       11.429
     23              12.222    0.050641    495    1.9648       12.123
     24              12.583     0.05064    495    1.9648       12.484
     25              14.562    0.050631    495    1.9648       14.462
     26              15.234    0.050627    495    1.9648       15.134
     27              15.439    0.050626    495    1.9648       15.339
     28              17.866    0.050614    495    1.9648       17.767
     29              18.451     0.05061    495    1.9648       18.352
     30              18.672    0.050609    495    1.9648       18.572
     31              18.941    0.050608    495    1.9648       18.841
     32              19.313    0.050605    495    1.9648       19.214
     33              21.537    0.050592    495    1.9648       21.438
     34              22.029    0.050589    495    1.9648        21.93
     35              22.084    0.050589    495    1.9648       21.985
     36              23.726    0.050578    495    1.9648       23.626
     37              23.898    0.050577    495    1.9648       23.799
     38              24.768    0.050571    495    1.9648       24.669
     39              25.666    0.050565    495    1.9648       25.567
     40              26.742    0.050558    495    1.9648       26.643
     41              26.878    0.050557    495    1.9648       26.778
     42              27.917     0.05055    495    1.9648       27.818
     43              28.236    0.050548    495    1.9648       28.136
     44              28.709    0.050544    495    1.9648       28.609
     45              29.071    0.050542    495    1.9648       28.972
     46              29.147    0.050541    495    1.9648       29.048
     47              29.347     0.05054    495    1.9648       29.248
     48              30.029    0.050535    495    1.9648       29.929
     49              31.394    0.050525    495    1.9648       31.294
     50               31.42    0.050525    495    1.9648       31.321
     51              31.474    0.050524    495    1.9648       31.375
     52               32.61    0.050516    495    1.9648       32.511
     53              33.764    0.050507    495    1.9648       33.665
     54              34.314    0.050503    495    1.9648       34.215
     55              34.963    0.050498    495    1.9648       34.863
     56              35.874    0.050492    495    1.9648       35.775
     57              36.064     0.05049    495    1.9648       35.964
     58              36.146     0.05049    495    1.9648       36.047
     59              36.252    0.050489    495    1.9648       36.153
     60              37.349    0.050481    495    1.9648        37.25
     61              37.806    0.050477    495    1.9648       37.707
     62              40.913    0.050454    495    1.9648       40.813
     63              41.717    0.050448    495    1.9648       41.618
     64              42.302    0.050444    495    1.9648       42.202
     65               43.79    0.050433    495    1.9648       43.691
     66              44.133     0.05043    495    1.9648       44.034
     67              44.428    0.050428    495    1.9648       44.328
     68              45.049    0.050424    495    1.9648        44.95
     69              45.139    0.050423    495    1.9648        45.04
     70              46.319    0.050414    495    1.9648        46.22
     71              46.688    0.050412    495    1.9648       46.589
     72                47.3    0.050408    495    1.9648       47.201
     73              48.416      0.0504    495    1.9648       48.317
     74              49.093    0.050395    495    1.9648       48.994
     75                49.2    0.050394    495    1.9648       49.101
     76              49.185    0.050395    495    1.9648       49.086
     77              49.439    0.050393    495    1.9648       49.339
     78              50.068    0.050389    495    1.9648       49.969
     79               50.64    0.050385    495    1.9648       50.541
     80               50.93    0.050383    495    1.9648       50.831
     81                51.3     0.05038    495    1.9648       51.201
     82              51.589    0.050378    495    1.9648       51.491
     83               53.06    0.050369    495    1.9648       52.961
     84              54.115    0.050363    495    1.9648       54.016
     85              54.781    0.050358    495    1.9648       54.682
     86              54.863    0.050358    495    1.9648       54.764
     87              55.305    0.050355    495    1.9648       55.207
     88              56.876    0.050346    495    1.9648       56.778
     89              57.989     0.05034    495    1.9648        57.89
     90              59.173    0.050334    495    1.9648       59.074
     91              59.263    0.050333    495    1.9648       59.164
     92              59.754    0.050331    495    1.9648       59.655
     93              60.315    0.050328    495    1.9648       60.216
     94              60.651    0.050326    495    1.9648       60.552
     95              60.975    0.050325    495    1.9648       60.876
     96              61.113    0.050324    495    1.9648       61.014
     97              61.651    0.050321    495    1.9648       61.552
     98               62.09    0.050319    495    1.9648       61.991
     99               62.96    0.050315    495    1.9648       62.861
    100              63.166    0.050315    495    1.9648       63.067
    101              63.206    0.050314    495    1.9648       63.107
    102              64.562    0.050309    495    1.9648       64.463
    103              66.405    0.050302    495    1.9648       66.306
    104              66.681    0.050301    495    1.9648       66.583
    105              67.888    0.050297    495    1.9648       67.789
    106              68.159    0.050296    495    1.9648        68.06
    107              68.225    0.050296    495    1.9648       68.126
    108              68.982    0.050293    495    1.9648       68.883
    109              69.668    0.050291    495    1.9648       69.569
    110              70.168     0.05029    495    1.9648       70.069
    111              71.875    0.050286    495    1.9648       71.776
    112              72.061    0.050286    495    1.9648       71.962
    113              72.185    0.050285    495    1.9648       72.086
    114              72.425    0.050285    495    1.9648       72.326
    115              72.342    0.050285    495    1.9648       72.243
    116              72.661    0.050284    495    1.9648       72.562
    117              72.611    0.050284    495    1.9648       72.512
    118              73.123    0.050284    495    1.9648       73.025
    119              75.022    0.050281    495    1.9648       74.923
    120              77.027    0.050279    495    1.9648       76.929
    121              77.711    0.050278    495    1.9648       77.613
    122              77.822    0.050278    495    1.9648       77.723
    123              77.908    0.050278    495    1.9648       77.809
    124               78.01    0.050278    495    1.9648       77.911
    125              78.693    0.050278    495    1.9648       78.594
    126                80.8    0.050278    495    1.9648       80.701
    127              81.399    0.050279    495    1.9648         81.3
    128              81.676    0.050279    495    1.9648       81.577
    129              81.891    0.050279    495    1.9648       81.792
    130              83.573    0.050281    495    1.9648       83.475
    131              85.331    0.050283    495    1.9648       85.232
    132              86.171    0.050285    495    1.9648       86.073
    133              86.226    0.050285    495    1.9648       86.127
    134              87.293    0.050287    495    1.9648       87.194
    135              87.392    0.050288    495    1.9648       87.293
    136              87.833    0.050289    495    1.9648       87.734
    137              88.944    0.050292    495    1.9648       88.845
    138              90.295    0.050296    495    1.9648       90.196
    139              90.601    0.050297    495    1.9648       90.502
    140              90.838    0.050298    495    1.9648       90.739
    141              91.198    0.050299    495    1.9648       91.099
    142              92.155    0.050302    495    1.9648       92.056
    143              92.363    0.050303    495    1.9648       92.264
    144              92.494    0.050303    495    1.9648       92.395
    145              92.706    0.050304    495    1.9648       92.607
    146              93.017    0.050306    495    1.9648       92.918
    147              93.721    0.050308    495    1.9648       93.622
    148              93.716    0.050308    495    1.9648       93.617
    149              94.088     0.05031    495    1.9648       93.989
    150              94.563    0.050312    495    1.9648       94.464
    151              95.296    0.050315    495    1.9648       95.197
    152              95.354    0.050316    495    1.9648       95.255
    153               95.85    0.050318    495    1.9648       95.751
    154              96.017    0.050319    495    1.9648       95.919
    155              96.767    0.050322    495    1.9648       96.668
    156              96.772    0.050322    495    1.9648       96.673
    157              97.024    0.050324    495    1.9648       96.925
    158              97.105    0.050324    495    1.9648       97.006
    159              97.625    0.050327    495    1.9648       97.527
    160              98.389    0.050331    495    1.9648        98.29
    161              101.08    0.050346    495    1.9648       100.98
    162              101.36    0.050348    495    1.9648       101.26
    163              101.96    0.050351    495    1.9648       101.86
    164              104.15    0.050365    495    1.9648       104.05
    165              107.96    0.050392    495    1.9648       107.86
    166              108.09    0.050392    495    1.9648       107.99
    167              108.45    0.050395    495    1.9648       108.35
    168              108.55    0.050396    495    1.9648       108.45
    169              108.94    0.050399    495    1.9648       108.84
    170              109.13      0.0504    495    1.9648       109.03
    171              109.47    0.050403    495    1.9648       109.37
    172              109.86    0.050406    495    1.9648       109.76
    173              110.24    0.050408    495    1.9648       110.14
    174              111.65    0.050419    495    1.9648       111.55
    175              111.72     0.05042    495    1.9648       111.62
    176               112.5    0.050426    495    1.9648        112.4
    177              113.07     0.05043    495    1.9648       112.97
    178              115.26    0.050448    495    1.9648       115.16
    179              116.15    0.050455    495    1.9648       116.05
    180              118.94    0.050478    495    1.9648       118.85
    181              119.15     0.05048    495    1.9648       119.05
    182              119.18     0.05048    495    1.9648       119.08
    183              119.31    0.050481    495    1.9648       119.21
    184              119.45    0.050482    495    1.9648       119.35
    185              120.14    0.050488    495    1.9648       120.04
    186              120.73    0.050492    495    1.9648       120.63
    187              121.04    0.050495    495    1.9648       120.95
    188              121.25    0.050497    495    1.9648       121.15
    189              122.27    0.050505    495    1.9648       122.17
    190              122.37    0.050506    495    1.9648       122.27
    191              122.57    0.050508    495    1.9648       122.47
    192              123.01    0.050511    495    1.9648       122.91
    193              123.96    0.050519    495    1.9648       123.86
    194              124.15    0.050521    495    1.9648       124.05
    195              125.39    0.050531    495    1.9648       125.29
    196              125.86    0.050534    495    1.9648       125.76
    197              127.01    0.050544    495    1.9648       126.91
    198              128.59    0.050556    495    1.9648       128.49
    199               129.3    0.050561    495    1.9648        129.2
    200              129.44    0.050563    495    1.9648       129.34
    201              130.44     0.05057    495    1.9648       130.34
    202              131.02    0.050575    495    1.9648       130.92
    203              131.03    0.050575    495    1.9648       130.93
    204              131.39    0.050577    495    1.9648       131.29
    205              131.42    0.050578    495    1.9648       131.32
    206                 132    0.050582    495    1.9648        131.9
    207              133.86    0.050595    495    1.9648       133.76
    208              134.77    0.050602    495    1.9648       134.67
    209              135.81    0.050609    495    1.9648       135.71
    210               137.6     0.05062    495    1.9648        137.5
    211              138.32    0.050625    495    1.9648       138.22
    212              138.83    0.050628    495    1.9648       138.73
    213               139.4    0.050631    495    1.9648       139.31
    214              140.42    0.050637    495    1.9648       140.32
    215              140.81    0.050639    495    1.9648       140.71
    216              140.82     0.05064    495    1.9648       140.72
    217              140.89     0.05064    495    1.9648       140.79
    218              140.86     0.05064    495    1.9648       140.76
    219              142.32    0.050648    495    1.9648       142.22
    220              142.88     0.05065    495    1.9648       142.78
    221              143.34    0.050653    495    1.9648       143.24
    222              143.36    0.050653    495    1.9648       143.26
    223              144.71    0.050659    495    1.9648       144.61
    224              146.81    0.050668    495    1.9648       146.72
    225              147.27     0.05067    495    1.9648       147.17
    226              147.59    0.050671    495    1.9648       147.49
    227              148.18    0.050673    495    1.9648       148.08
    228              148.69    0.050675    495    1.9648       148.59
    229              149.24    0.050677    495    1.9648       149.14
    230              149.38    0.050677    495    1.9648       149.28
    231              149.84    0.050679    495    1.9648       149.74
    232              151.06    0.050682    495    1.9648       150.96
    233              151.29    0.050683    495    1.9648       151.19
    234              151.37    0.050683    495    1.9648       151.27
    235              151.57    0.050684    495    1.9648       151.47
    236              153.05    0.050687    495    1.9648       152.95
    237              153.34    0.050688    495    1.9648       153.24
    238              154.51     0.05069    495    1.9648       154.41
    239              154.46     0.05069    495    1.9648       154.36
    240              154.93     0.05069    495    1.9648       154.83
    241              155.09    0.050691    495    1.9648       154.99
    242              155.27    0.050691    495    1.9648       155.17
    243              155.32    0.050691    495    1.9648       155.22
    244              156.26    0.050692    495    1.9648       156.16
    245              157.73    0.050693    495    1.9648       157.63
    246               157.9    0.050693    495    1.9648        157.8
    247              -158.2    0.050693    495    1.9648       -158.3
    248              -157.1    0.050693    495    1.9648       -157.2
    249             -156.82    0.050693    495    1.9648      -156.92
    250             -156.26    0.050693    495    1.9648      -156.36
    251             -155.46    0.050693    495    1.9648      -155.56
    252             -155.01    0.050692    495    1.9648      -155.11
    253             -154.71    0.050692    495    1.9648      -154.81
    254             -154.51    0.050692    495    1.9648      -154.61
    255             -154.33    0.050692    495    1.9648      -154.43
    256             -153.62    0.050691    495    1.9648      -153.72
    257             -152.81     0.05069    495    1.9648      -152.91
    258             -152.73     0.05069    495    1.9648      -152.83
    259             -150.77    0.050686    495    1.9648      -150.87
    260             -150.11    0.050684    495    1.9648      -150.21
    261             -149.84    0.050684    495    1.9648      -149.94
    262             -148.88    0.050681    495    1.9648      -148.98
    263             -147.97    0.050678    495    1.9648      -148.07
    264             -147.78    0.050678    495    1.9648      -147.88
    265             -146.57    0.050674    495    1.9648      -146.67
    266             -146.58    0.050674    495    1.9648      -146.67
    267             -145.09    0.050668    495    1.9648      -145.19
    268             -143.16     0.05066    495    1.9648      -143.26
    269             -143.05     0.05066    495    1.9648      -143.15
    270             -142.93    0.050659    495    1.9648      -143.03
    271             -141.68    0.050653    495    1.9648      -141.78
    272             -141.55    0.050652    495    1.9648      -141.65
    273             -141.21    0.050651    495    1.9648      -141.31
    274             -140.84    0.050649    495    1.9648      -140.94
    275              -140.7    0.050648    495    1.9648       -140.8
    276              -139.8    0.050643    495    1.9648       -139.9
    277             -138.69    0.050637    495    1.9648      -138.79
    278             -138.65    0.050637    495    1.9648      -138.75
    279             -137.09    0.050628    495    1.9648      -137.19
    280             -136.74    0.050626    495    1.9648      -136.84
    281             -136.42    0.050624    495    1.9648      -136.52
    282             -136.16    0.050622    495    1.9648      -136.26
    283             -135.59    0.050618    495    1.9648      -135.69
    284              -135.2    0.050616    495    1.9648       -135.3
    285             -134.35     0.05061    495    1.9648      -134.45
    286             -134.18    0.050609    495    1.9648      -134.28
    287             -134.03    0.050608    495    1.9648      -134.13
    288             -132.55    0.050598    495    1.9648      -132.65
    289              -132.6    0.050598    495    1.9648       -132.7
    290             -131.06    0.050587    495    1.9648      -131.16
    291              -130.6    0.050584    495    1.9648      -130.69
    292             -130.28    0.050582    495    1.9648      -130.38
    293             -129.91    0.050579    495    1.9648      -130.01
    294             -126.83    0.050555    495    1.9648      -126.93
    295             -126.84    0.050555    495    1.9648      -126.94
    296             -126.73    0.050554    495    1.9648      -126.82
    297             -126.29    0.050551    495    1.9648      -126.39
    298             -125.73    0.050547    495    1.9648      -125.83
    299             -125.34    0.050543    495    1.9648      -125.44
    300             -125.26    0.050543    495    1.9648      -125.36
    301              -123.3    0.050527    495    1.9648       -123.4
    302             -123.13    0.050526    495    1.9648      -123.23
    303             -122.88    0.050523    495    1.9648      -122.98
    304             -121.26     0.05051    495    1.9648      -121.36
    305              -120.7    0.050505    495    1.9648       -120.8
    306             -119.75    0.050498    495    1.9648      -119.85
    307             -119.04    0.050492    495    1.9648      -119.14
    308             -118.83     0.05049    495    1.9648      -118.93
    309             -118.07    0.050484    495    1.9648      -118.17
    310             -117.81    0.050481    495    1.9648      -117.91
    311             -117.76    0.050481    495    1.9648      -117.86
    312             -117.69     0.05048    495    1.9648      -117.79
    313              -116.4     0.05047    495    1.9648      -116.49
    314              -116.2    0.050468    495    1.9648       -116.3
    315             -116.04    0.050467    495    1.9648      -116.14
    316             -115.79    0.050465    495    1.9648      -115.89
    317             -115.16    0.050459    495    1.9648      -115.26
    318             -115.02    0.050458    495    1.9648      -115.12
    319              -114.4    0.050453    495    1.9648       -114.5
    320             -113.68    0.050447    495    1.9648      -113.78
    321             -113.27    0.050444    495    1.9648      -113.37
    322              -112.5    0.050437    495    1.9648       -112.6
    323             -112.45    0.050437    495    1.9648      -112.55
    324             -111.84    0.050432    495    1.9648      -111.94
    325             -110.54    0.050422    495    1.9648      -110.64
    326             -110.39     0.05042    495    1.9648      -110.49
    327             -109.83    0.050416    495    1.9648      -109.93
    328             -106.52    0.050391    495    1.9648      -106.62
    329             -105.39    0.050382    495    1.9648      -105.49
    330             -105.42    0.050383    495    1.9648      -105.52
    331             -105.19    0.050381    495    1.9648      -105.29
    332             -105.15    0.050381    495    1.9648      -105.25
    333             -102.96    0.050365    495    1.9648      -103.06
    334             -102.34    0.050361    495    1.9648      -102.44
    335             -100.06    0.050346    495    1.9648      -100.16
    336             -100.06    0.050346    495    1.9648      -100.15
    337             -100.08    0.050347    495    1.9648      -100.18
    338             -99.652    0.050344    495    1.9648      -99.751
    339             -98.955     0.05034    495    1.9648      -99.054
    340             -97.781    0.050333    495    1.9648       -97.88
    341             -97.701    0.050332    495    1.9648        -97.8
    342             -96.387    0.050325    495    1.9648      -96.486
    343             -96.305    0.050325    495    1.9648      -96.404
    344             -95.575    0.050321    495    1.9648      -95.674
    345             -95.055    0.050318    495    1.9648      -95.153
    346             -95.002    0.050318    495    1.9648      -95.101
    347             -94.945    0.050318    495    1.9648      -95.044
    348             -93.623    0.050311    495    1.9648      -93.722
    349             -93.442    0.050311    495    1.9648      -93.541
    350             -93.099    0.050309    495    1.9648      -93.198
    351             -92.918    0.050308    495    1.9648      -93.017
    352             -92.823    0.050308    495    1.9648      -92.922
    353             -92.358    0.050306    495    1.9648      -92.456
    354             -91.867    0.050304    495    1.9648      -91.965
    355             -90.742      0.0503    495    1.9648       -90.84
    356             -90.466    0.050298    495    1.9648      -90.565
    357             -90.335    0.050298    495    1.9648      -90.434
    358             -89.406    0.050295    495    1.9648      -89.505
    359             -87.913     0.05029    495    1.9648      -88.012
    360             -87.013    0.050288    495    1.9648      -87.112
    361             -86.623    0.050287    495    1.9648      -86.722
    362             -85.302    0.050284    495    1.9648      -85.401
    363             -85.052    0.050283    495    1.9648      -85.151
    364             -83.246     0.05028    495    1.9648      -83.344
    365             -82.833     0.05028    495    1.9648      -82.932
    366             -80.619    0.050278    495    1.9648      -80.718
    367             -80.548    0.050278    495    1.9648      -80.646
    368             -79.963    0.050278    495    1.9648      -80.062
    369             -78.842    0.050278    495    1.9648       -78.94
    370             -78.542    0.050278    495    1.9648      -78.641
    371             -77.545    0.050279    495    1.9648      -77.643
    372             -77.292    0.050279    495    1.9648      -77.391
    373             -76.798    0.050279    495    1.9648      -76.897
    374             -73.831    0.050283    495    1.9648       -73.93
    375             -73.175    0.050284    495    1.9648      -73.274
    376             -72.934    0.050285    495    1.9648      -73.033
    377              -72.77    0.050285    495    1.9648      -72.868
    378             -72.312    0.050286    495    1.9648      -72.411
    379             -72.253    0.050287    495    1.9648      -72.351
    380             -72.058    0.050287    495    1.9648      -72.156
    381             -71.549    0.050288    495    1.9648      -71.648
    382             -70.909     0.05029    495    1.9648      -71.008
    383              -70.36    0.050292    495    1.9648      -70.458
    384             -69.997    0.050293    495    1.9648      -70.096
    385             -69.691    0.050294    495    1.9648      -69.789
    386             -68.277    0.050299    495    1.9648      -68.376
    387             -68.051    0.050299    495    1.9648       -68.15
    388             -65.831    0.050308    495    1.9648       -65.93
    389             -65.255    0.050311    495    1.9648      -65.353
    390             -65.192    0.050311    495    1.9648      -65.291
    391             -64.898    0.050313    495    1.9648      -64.996
    392             -64.877    0.050313    495    1.9648      -64.976
    393             -64.253    0.050316    495    1.9648      -64.352
    394             -62.638    0.050324    495    1.9648      -62.737
    395             -61.842    0.050328    495    1.9648      -61.941
    396             -61.414     0.05033    495    1.9648      -61.513
    397             -61.336    0.050331    495    1.9648      -61.435
    398             -60.632    0.050335    495    1.9648      -60.731
    399              -59.93    0.050339    495    1.9648      -60.029
    400             -59.757     0.05034    495    1.9648      -59.856
    401             -59.022    0.050345    495    1.9648      -59.121
    402              -58.54    0.050347    495    1.9648      -58.639
    403             -58.097     0.05035    495    1.9648      -58.196
    404              -56.92    0.050358    495    1.9648      -57.019
    405             -56.354    0.050362    495    1.9648      -56.453
    406             -54.924    0.050371    495    1.9648      -55.023
    407              -54.77    0.050373    495    1.9648      -54.869
    408             -54.567    0.050374    495    1.9648      -54.666
    409             -54.078    0.050377    495    1.9648      -54.177
    410             -53.902    0.050379    495    1.9648      -54.001
    411             -53.472    0.050382    495    1.9648      -53.571
    412             -53.381    0.050382    495    1.9648       -53.48
    413              -52.22    0.050391    495    1.9648      -52.319
    414             -51.825    0.050394    495    1.9648      -51.924
    415             -50.928    0.050401    495    1.9648      -51.027
    416              -49.55    0.050411    495    1.9648      -49.649
    417             -49.071    0.050415    495    1.9648       -49.17
    418             -47.365    0.050428    495    1.9648      -47.464
    419             -46.347    0.050437    495    1.9648      -46.446
    420             -45.955     0.05044    495    1.9648      -46.054
    421             -45.782    0.050441    495    1.9648      -45.881
    422             -45.119    0.050446    495    1.9648      -45.218
    423              -44.62     0.05045    495    1.9648      -44.719
    424             -43.995    0.050456    495    1.9648      -44.094
    425             -43.988    0.050456    495    1.9648      -44.088
    426             -43.977    0.050456    495    1.9648      -44.076
    427             -43.771    0.050457    495    1.9648       -43.87
    428               -43.3    0.050461    495    1.9648      -43.399
    429             -42.549    0.050467    495    1.9648      -42.648
    430             -42.213     0.05047    495    1.9648      -42.312
    431             -41.992    0.050472    495    1.9648      -42.091
    432             -40.018    0.050488    495    1.9648      -40.117
    433             -39.206    0.050495    495    1.9648      -39.305
    434              -38.77    0.050498    495    1.9648       -38.87
    435             -38.001    0.050504    495    1.9648        -38.1
    436             -37.058    0.050512    495    1.9648      -37.157
    437             -36.708    0.050515    495    1.9648      -36.808
    438             -36.607    0.050516    495    1.9648      -36.706
    439             -36.629    0.050515    495    1.9648      -36.728
    440             -36.251    0.050518    495    1.9648      -36.351
    441             -36.266    0.050518    495    1.9648      -36.366
    442             -36.099     0.05052    495    1.9648      -36.198
    443             -35.435    0.050525    495    1.9648      -35.535
    444             -34.056    0.050536    495    1.9648      -34.156
    445             -33.746    0.050538    495    1.9648      -33.845
    446             -33.288    0.050542    495    1.9648      -33.387
    447             -31.231    0.050557    495    1.9648       -31.33
    448             -30.744    0.050561    495    1.9648      -30.843
    449             -28.851    0.050574    495    1.9648      -28.951
    450              -28.67    0.050576    495    1.9648      -28.769
    451             -28.161    0.050579    495    1.9648      -28.261
    452             -27.516    0.050584    495    1.9648      -27.615
    453             -27.422    0.050584    495    1.9648      -27.521
    454             -27.018    0.050587    495    1.9648      -27.117
    455             -26.858    0.050588    495    1.9648      -26.957
    456             -26.467    0.050591    495    1.9648      -26.567
    457             -26.485    0.050591    495    1.9648      -26.584
    458             -25.779    0.050595    495    1.9648      -25.878
    459             -25.579    0.050597    495    1.9648      -25.678
    460             -24.753    0.050602    495    1.9648      -24.853
    461             -24.674    0.050602    495    1.9648      -24.774
    462             -23.737    0.050608    495    1.9648      -23.836
    463             -21.611     0.05062    495    1.9648       -21.71
    464             -21.278    0.050622    495    1.9648      -21.378
    465             -20.421    0.050627    495    1.9648       -20.52
    466             -20.433    0.050627    495    1.9648      -20.532
    467             -20.459    0.050626    495    1.9648      -20.558
    468              -19.97    0.050629    495    1.9648      -20.069
    469             -19.171    0.050633    495    1.9648       -19.27
    470             -18.893    0.050634    495    1.9648      -18.992
    471             -18.755    0.050635    495    1.9648      -18.855
    472             -17.862    0.050639    495    1.9648      -17.961
    473             -17.942    0.050639    495    1.9648      -18.042
    474             -17.511    0.050641    495    1.9648      -17.611
    475             -17.511    0.050641    495    1.9648      -17.611
    476             -16.941    0.050643    495    1.9648      -17.041
    477             -16.598    0.050645    495    1.9648      -16.697
    478             -16.493    0.050645    495    1.9648      -16.592
    479             -16.414    0.050646    495    1.9648      -16.513
    480              -14.21    0.050654    495    1.9648      -14.309
    481             -14.021    0.050655    495    1.9648      -14.121
    482             -13.045    0.050658    495    1.9648      -13.144
    483             -12.452     0.05066    495    1.9648      -12.552
    484             -11.314    0.050663    495    1.9648      -11.414
    485             -10.775    0.050664    495    1.9648      -10.875
    486             -10.202    0.050666    495    1.9648      -10.301
    487             -9.9277    0.050666    495    1.9648      -10.027
    488             -9.8317    0.050667    495    1.9648      -9.9312
    489             -9.3933    0.050668    495    1.9648      -9.4928
    490             -9.2314    0.050668    495    1.9648       -9.331
    491             -8.2837     0.05067    495    1.9648      -8.3832
    492             -7.0638    0.050672    495    1.9648      -7.1633
    493             -6.4429    0.050672    495    1.9648      -6.5424
    494             -4.8267    0.050674    495    1.9648      -4.9262
    495             -4.5049    0.050674    495    1.9648      -4.6045
    496             -3.7284    0.050674    495    1.9648       -3.828
    497             -2.5452    0.050674    495    1.9648      -2.6448
    498             -2.0393    0.050674    495    1.9648      -2.1389
    499             -1.3021    0.050674    495    1.9648      -1.4017
    500            -0.93418    0.050674    495    1.9648      -1.0337


     UPPER  
    ________

       0.166
     0.37769
      0.8323
      1.2794
      1.3576
      1.4761
      2.0408
      2.8535
      3.6029
      4.3996
      4.7085
      5.3947
      5.4382
      5.4533
      5.8285
      5.7805
      7.1518
      7.1978
      7.2705
      8.6724
      10.049
      11.628
      12.322
      12.683
      14.661
      15.333
      15.538
      17.966
      18.551
      18.771
       19.04
      19.413
      21.637
      22.129
      22.184
      23.825
      23.998
      24.868
      25.765
      26.842
      26.977
      28.017
      28.335
      28.808
       29.17
      29.247
      29.446
      30.128
      31.493
      31.519
      31.574
      32.709
      33.864
      34.413
      35.062
      35.973
      36.163
      36.245
      36.351
      37.448
      37.905
      41.012
      41.816
      42.401
      43.889
      44.233
      44.527
      45.149
      45.238
      46.418
      46.787
      47.399
      48.515
      49.192
      49.299
      49.284
      49.538
      50.167
      50.739
      51.029
      51.399
      51.688
      53.159
      54.214
       54.88
      54.962
      55.404
      56.975
      58.088
      59.271
      59.362
      59.853
      60.414
       60.75
      61.074
      61.212
       61.75
      62.189
      63.059
      63.264
      63.305
      64.661
      66.504
       66.78
      67.987
      68.258
      68.323
      69.081
      69.767
      70.266
      71.974
       72.16
      72.284
      72.524
      72.441
       72.76
       72.71
      73.222
      75.121
      77.126
       77.81
       77.92
      78.007
      78.109
      78.792
      80.899
      81.498
      81.774
       81.99
      83.672
       85.43
       86.27
      86.325
      87.391
       87.49
      87.932
      89.043
      90.394
        90.7
      90.937
      91.297
      92.254
      92.462
      92.593
      92.805
      93.116
      93.819
      93.815
      94.187
      94.662
      95.395
      95.453
      95.949
      96.116
      96.866
      96.871
      97.123
      97.204
      97.724
      98.488
      101.17
      101.46
      102.06
      104.25
      108.06
      108.19
      108.55
      108.65
      109.03
      109.23
      109.57
      109.96
      110.34
      111.74
      111.81
       112.6
      113.17
      115.36
      116.25
      119.04
      119.25
      119.27
      119.41
      119.55
      120.24
      120.83
      121.14
      121.35
      122.36
      122.46
      122.67
      123.11
      124.06
      124.25
      125.49
      125.96
      127.11
      128.69
      129.39
      129.54
      130.54
      131.12
      131.13
      131.49
      131.52
       132.1
      133.96
      134.87
       135.9
       137.7
      138.42
      138.92
       139.5
      140.52
      140.91
      140.92
      140.99
      140.96
      142.42
      142.97
      143.44
      143.46
      144.81
      146.91
      147.37
      147.69
      148.28
      148.79
      149.33
      149.48
      149.94
      151.16
      151.39
      151.47
      151.67
      153.15
      153.44
      154.61
      154.56
      155.03
      155.19
      155.37
      155.42
      156.36
      157.83
         158
     -158.11
        -157
     -156.72
     -156.16
     -155.36
     -154.92
     -154.61
     -154.41
     -154.23
     -153.52
     -152.71
     -152.63
     -150.67
     -150.01
     -149.74
     -148.78
     -147.87
     -147.68
     -146.47
     -146.48
     -144.99
     -143.06
     -142.95
     -142.83
     -141.58
     -141.45
     -141.11
     -140.74
      -140.6
      -139.7
     -138.59
     -138.55
     -136.99
     -136.64
     -136.32
     -136.06
     -135.49
      -135.1
     -134.25
     -134.08
     -133.93
     -132.45
      -132.5
     -130.96
      -130.5
     -130.18
     -129.81
     -126.73
     -126.74
     -126.63
     -126.19
     -125.63
     -125.24
     -125.16
      -123.2
     -123.03
     -122.78
     -121.16
      -120.6
     -119.65
     -118.94
     -118.73
     -117.98
     -117.71
     -117.66
     -117.59
      -116.3
      -116.1
     -115.94
     -115.69
     -115.06
     -114.92
      -114.3
     -113.58
     -113.17
      -112.4
     -112.36
     -111.74
     -110.44
     -110.29
     -109.73
     -106.42
     -105.29
     -105.33
     -105.09
     -105.05
     -102.86
     -102.24
     -99.965
     -99.957
     -99.981
     -99.553
     -98.856
     -97.682
     -97.602
     -96.288
     -96.206
     -95.476
     -94.956
     -94.903
     -94.846
     -93.524
     -93.343
     -93.001
     -92.819
     -92.724
     -92.259
     -91.768
     -90.643
     -90.367
     -90.236
     -89.307
     -87.814
     -86.915
     -86.524
     -85.203
     -84.953
     -83.147
     -82.734
      -80.52
     -80.449
     -79.864
     -78.743
     -78.443
     -77.446
     -77.193
       -76.7
     -73.732
     -73.076
     -72.835
     -72.671
     -72.213
     -72.154
     -71.959
      -71.45
      -70.81
     -70.261
     -69.898
     -69.592
     -68.179
     -67.952
     -65.732
     -65.156
     -65.094
     -64.799
     -64.778
     -64.155
     -62.539
     -61.743
     -61.315
     -61.237
     -60.533
     -59.831
     -59.658
     -58.923
     -58.441
     -57.998
     -56.821
     -56.255
     -54.825
     -54.671
     -54.468
     -53.979
     -53.803
     -53.373
     -53.282
     -52.121
     -51.726
     -50.829
     -49.451
     -48.972
     -47.266
     -46.248
     -45.856
     -45.683
      -45.02
     -44.521
     -43.896
     -43.889
     -43.878
     -43.672
     -43.201
     -42.449
     -42.114
     -41.893
     -39.918
     -39.106
     -38.671
     -37.902
     -36.958
     -36.609
     -36.508
      -36.53
     -36.152
     -36.167
         -36
     -35.336
     -33.957
     -33.646
     -33.188
     -31.132
     -30.644
     -28.752
      -28.57
     -28.062
     -27.416
     -27.322
     -26.918
     -26.758
     -26.368
     -26.386
     -25.679
      -25.48
     -24.654
     -24.575
     -23.637
     -21.512
     -21.179
     -20.321
     -20.333
     -20.359
      -19.87
     -19.071
     -18.793
     -18.656
     -17.762
     -17.843
     -17.412
     -17.412
     -16.842
     -16.498
     -16.393
     -16.314
      -14.11
     -13.922
     -12.945
     -12.353
     -11.215
     -10.676
     -10.102
     -9.8281
     -9.7321
     -9.2937
     -9.1319
     -8.1841
     -6.9642
     -6.3433
     -4.7271
     -4.4053
     -3.6289
     -2.4457
     -1.9398
     -1.2025
    -0.83462

Displacement unit: nanometer [nm]

Plot the stat. uncertainty of displacement

displ_std = result.Displacement_std;

figure
plot(phitrue, displ_std)
xlabel('phi');
ylabel(['Statistical uncertainty of displacement, ',result.Displacement_unit]);
title(['Statistical Uncertainty: Min: ', ...
    num2str(result.Displacement_std_min), ', Max: ', ...
    num2str(result.Displacement_std_max) ]);

Plot the displacements with expanded uncertainties

displ_fit = result.Displacement_fit;
const = result.Displacement_const;
displ_true = const*phitrue;
displ_res = displ_fit - displ_true;
ix = (result.phi_fit-phitrue) < -1;
displ_res(ix) = displ_res(ix) + 2*pi*const;

figure
plot(displ_true, displ_res ,'o')
hold
plot(displ_true, 2*displ_std ,'r-')
plot(displ_true, -2*displ_std ,'r-')
grid
xlabel('True displacement');
ylabel('Displacement Residuals');
title('Expanded Uncertainty of Fitted Displacement');
Current plot held

Plot the X residuals with the expanded uncertainties

figure
plot(phitrue,result.x_res_fit,'.')
hold
plot(phitrue,2*result.x_res_std,'r-')
plot(phitrue,-2*result.x_res_std,'r-')
grid
xlabel('True phi');
ylabel('x residuals');
title('Expanded Uncertainty of Fitted X Residuals');
Current plot held

Plot the Y residuals with the expanded uncertainties

figure
plot(phitrue,result.y_res_fit,'.')
hold
plot(phitrue,2*result.y_res_std,'r-')
plot(phitrue,-2*result.y_res_std,'r-')
grid
xlabel('True phi');
ylabel('y residuals');
title('Expanded Uncertainty of Fitted Y Residuals');
Current plot held

CORRELATED MEASUREMENTS

clear

GENERATE the correlated measurements: x and y

alpha0true = 0;                             % x-center (offset x)
beta0true  = 0;                             % y-center (offset x)
alpha1true = 1;                             % x-amplitude
beta1true  = 0.98;                             % y-amplitude
phi0true   = pi/10;                         % phase offset

sigma = 0.005;                           % std of x and y independent errors
n = 1000;                               % number of measurements points
cycles = 1;                             % measurement interval,  # cycles
phitrue = cycles*(2*pi)*sort(rand(n,1));    % true phases phi_i

% true values:  X and Y
Xmean = @(t) alpha0true + alpha1true * cos(t);
Ymean = @(t) beta0true + beta1true * sin(t + phi0true);

rho = 0.9;
err = mvnrnd([0 0],sigma^2*[1 rho; rho 1],n);

% AR errors + correlated x and y
% rhoAR = -.99995;
% err = sigma*filter(1,[1 rhoAR],mvnrnd([0 0],[1 rho; rho 1],n));

x = Xmean(phitrue) + err(:,1);
y = Ymean(phitrue) + err(:,2);

Fit the ellipse based on measured data

options.alpha = 0.05;
options.correlation = rho; % Set the true correlation (assumed to be known)
options.displconst = 633.3/(4*pi);
options.displunit = 'nanometer [nm]';
result = ellipseFit4HC(x,y,options);

disp(result)
  -------------------------------------------------
  ESTIMATED ELLIPSE PARAMETERS                     
  X^2 + B*Y^2 + C*X*Y + D*X + F*Y + G = 0          
  -------------------------------------------------
          ESTIMATE        STD        DF     FACTOR       LOWER         UPPER   
         __________    __________    ___    ______    ___________    __________

    B        1.0403    0.00071011    995    1.9624          1.039        1.0417
    C      -0.63017    0.00071325    995    1.9624       -0.63157      -0.62877
    D    8.6817e-05    0.00031468    995    1.9624    -0.00053069    0.00070433
    F    0.00015771    0.00032069    995    1.9624    -0.00047159    0.00078702
    G      -0.90401    0.00037431    995    1.9624       -0.90475      -0.90328

  -------------------------------------------------
  ESTIMATED ELLIPSE PARAMETERS                     
  X(phi) = alpha_0 + alpha_1 * cos(phi)            
  Y(phi) = beta_0  + beta_1  * sin(phi + phi_0     
  -------------------------------------------------
                ESTIMATE         STD        DF     FACTOR       LOWER   
               ___________    __________    ___    ______    ___________

    alpha_0    -7.4391e-05    0.00019574    995    1.9624     -0.0004585
    beta_0     -9.8329e-05    0.00019179    995    1.9624    -0.00047468
    alpha_1        0.99969    0.00025686    995    1.9624        0.99919
    beta_1         0.98011    0.00024759    995    1.9624        0.97963
    phi_0          0.31405    0.00034675    995    1.9624        0.31337


                 UPPER   
               __________

    alpha_0    0.00030972
    beta_0     0.00027803
    alpha_1        1.0002
    beta_1         0.9806
    phi_0         0.31473

                  Description: 'Ellipse Fit by Iterated Locally Best Linea...'
           ABCDEF_Description: 'A*x^2 + 2*B*x*y + C*y^2 + 2*D*x + 2*E*y + ...'
                 ABCDEF_Names: {'A'  'B'  'C'  'D'  'E'  'F'}
                   ABCDEF_fit: [1x6 double]
                   ABCDEF_std: [1x6 double]
            BCDFG_Description: 'x^2 + B*y^2 +  C*x*y + D*x + F*y + G = 0'
                  BCDFG_Names: {'B'  'C'  'D'  'F'  'G'}
                    BCDFG_fit: [1.0403 -0.6302 8.6817e-05 1.5771e-04 -0.9040]
                    BCDFG_std: [1x5 double]
                    BCDFG_cov: [5x5 double]
    EllipsePars_Description_X: 'X(phi) = alpha_0 + alpha_1 * cos(phi)'
    EllipsePars_Description_Y: 'Y(phi) = beta_0  + beta_1  * sin(phi + phi_0)'
            EllipsePars_Names: {1x5 cell}
              EllipsePars_fit: [-7.4391e-05 -9.8329e-05 0.9997 0.9801 0.3140]
              EllipsePars_std: [1x5 double]
                     mu_X_fit: [1000x1 double]
                     mu_X_std: [1000x1 double]
                     nu_Y_fit: [1000x1 double]
                     nu_Y_std: [1000x1 double]
                     X_fitfun: @(t)alpha0_fit+alpha1_fit*cos(t)
                     Y_fitfun: @(t)beta0_fit+beta1_fit*sin(t+phi0_fit)
                    x_res_fit: [1000x1 double]
                    x_res_std: [1000x1 double]
                    y_res_fit: [1000x1 double]
                    y_res_std: [1000x1 double]
                    sigma_fit: 0.0051
                   sigma2_fit: 2.5536e-05
                      phi_fit: [1000x1 double]
                      phi_std: [1000x1 double]
                  phi_std_max: 0.0062
                  phi_std_min: 0.0020
     Displacement_Description: 'Displacement_fit = Displacement_const * ph...'
             Displacement_fit: [1000x1 double]
             Displacement_std: [1000x1 double]
         Displacement_std_max: 0.3104
         Displacement_std_min: 0.0991
           Displacement_const: 50.3964
            Displacement_unit: 'nanometer [nm]'
                  TABLE_BCDFG: [5x6 table]
            TABLE_EllipsePars: [5x6 table]
          TABLE_Displacements: [1000x7 table]
                       x_data: [1000x1 double]
                       y_data: [1000x1 double]
          used_Correlation_XY: 0.9000
                      options: [1x1 struct]
                    criterion: 2.1270e-12
                        loops: 7
                       tictoc: 0.0255

Display statistics of the fitted displacements (!! Table with n rows !!)

TABLE1 = result.TABLE_EllipsePars;
TABLE2 = result.TABLE_Displacements;

disp(TABLE2)
disp(['Displacement unit: ' result.Displacement_unit])
    OBSERVATION    ESTIMATE      STD       DF     FACTOR     LOWER      UPPER 
    ___________    ________    ________    ___    ______    _______    _______

       1            1.2196      0.11976    995    1.9624    0.98454     1.4546
       2            2.0558      0.11858    995    1.9624     1.8231     2.2885
       3            2.3752      0.11815    995    1.9624     2.1433      2.607
       4            4.1426      0.11584    995    1.9624     3.9153     4.3699
       5            4.4604      0.11545    995    1.9624     4.2339      4.687
       6            4.8572      0.11497    995    1.9624     4.6316     5.0828
       7            4.6004      0.11528    995    1.9624     4.3742     4.8266
       8              4.59      0.11529    995    1.9624     4.3638     4.8163
       9            4.6821      0.11518    995    1.9624     4.4561     4.9081
      10            5.0404      0.11475    995    1.9624     4.8153     5.2656
      11            5.0176      0.11477    995    1.9624     4.7923     5.2428
      12             5.553      0.11414    995    1.9624      5.329      5.777
      13            6.2602      0.11333    995    1.9624     6.0379     6.4826
      14            6.6402      0.11291    995    1.9624     6.4186     6.8617
      15            6.8591      0.11267    995    1.9624      6.638     7.0802
      16            7.2358      0.11226    995    1.9624     7.0155      7.456
      17            7.7238      0.11174    995    1.9624     7.5046     7.9431
      18            7.9199      0.11154    995    1.9624     7.7011     8.1388
      19             8.087      0.11137    995    1.9624     7.8684     8.3055
      20            7.9215      0.11154    995    1.9624     7.7026     8.1404
      21            8.4959      0.11095    995    1.9624     8.2781     8.7136
      22            8.5153      0.11093    995    1.9624     8.2976      8.733
      23            8.4272      0.11102    995    1.9624     8.2094     8.6451
      24            8.5857      0.11086    995    1.9624     8.3681     8.8032
      25            8.6625      0.11078    995    1.9624     8.4451     8.8799
      26            8.6875      0.11076    995    1.9624     8.4701     8.9048
      27            8.8788      0.11057    995    1.9624     8.6619     9.0958
      28             9.021      0.11043    995    1.9624     8.8043     9.2377
      29            8.8546      0.11059    995    1.9624     8.6376     9.0717
      30            8.8666      0.11058    995    1.9624     8.6496     9.0836
      31            8.9623      0.11049    995    1.9624     8.7455     9.1791
      32            9.2986      0.11016    995    1.9624     9.0824     9.5147
      33            9.9527      0.10954    995    1.9624     9.7378     10.168
      34            10.265      0.10925    995    1.9624     10.051      10.48
      35             10.04      0.10946    995    1.9624     9.8253     10.255
      36            10.654       0.1089    995    1.9624     10.441     10.868
      37            10.796      0.10877    995    1.9624     10.582     11.009
      38             10.87      0.10871    995    1.9624     10.657     11.084
      39            11.139      0.10847    995    1.9624     10.926     11.352
      40            11.322      0.10831    995    1.9624     11.109     11.534
      41            11.445       0.1082    995    1.9624     11.232     11.657
      42            11.825      0.10788    995    1.9624     11.614     12.037
      43            11.762      0.10793    995    1.9624      11.55     11.974
      44            11.864      0.10785    995    1.9624     11.652     12.075
      45            12.458      0.10736    995    1.9624     12.247     12.669
      46            13.059      0.10688    995    1.9624     12.849     13.269
      47            13.807       0.1063    995    1.9624     13.599     14.016
      48            14.243      0.10598    995    1.9624     14.035     14.451
      49             14.43      0.10584    995    1.9624     14.222     14.638
      50            14.949      0.10547    995    1.9624     14.742     15.156
      51            15.135      0.10534    995    1.9624     14.928     15.342
      52             15.07      0.10539    995    1.9624     14.863     15.277
      53            15.215      0.10528    995    1.9624     15.009     15.422
      54            15.175      0.10531    995    1.9624     14.968     15.381
      55            16.517      0.10442    995    1.9624     16.312     16.721
      56            16.642      0.10434    995    1.9624     16.437     16.847
      57            16.764      0.10426    995    1.9624      16.56     16.969
      58            17.022       0.1041    995    1.9624     16.818     17.226
      59            17.339      0.10391    995    1.9624     17.135     17.542
      60            17.462      0.10384    995    1.9624     17.258     17.666
      61            18.761      0.10309    995    1.9624     18.559     18.963
      62            19.044      0.10294    995    1.9624     18.842     19.246
      63            19.476      0.10271    995    1.9624     19.275     19.678
      64            19.516      0.10269    995    1.9624     19.314     19.717
      65            20.402      0.10225    995    1.9624     20.201     20.603
      66             21.67      0.10167    995    1.9624      21.47     21.869
      67            21.734      0.10164    995    1.9624     21.535     21.934
      68            22.057      0.10151    995    1.9624     21.858     22.257
      69            22.146      0.10147    995    1.9624     21.947     22.345
      70            21.972      0.10154    995    1.9624     21.773     22.171
      71            22.543      0.10131    995    1.9624     22.345     22.742
      72            22.548       0.1013    995    1.9624     22.349     22.747
      73            22.738      0.10123    995    1.9624      22.54     22.937
      74            23.023      0.10112    995    1.9624     22.824     23.221
      75            23.351        0.101    995    1.9624     23.152     23.549
      76            23.358      0.10099    995    1.9624      23.16     23.556
      77            23.445      0.10096    995    1.9624     23.247     23.644
      78            23.469      0.10095    995    1.9624     23.271     23.667
      79            24.499      0.10059    995    1.9624     24.302     24.697
      80            24.652      0.10054    995    1.9624     24.455      24.85
      81            25.009      0.10043    995    1.9624     24.812     25.206
      82            25.581      0.10026    995    1.9624     25.384     25.778
      83            25.683      0.10023    995    1.9624     25.487      25.88
      84            25.987      0.10015    995    1.9624      25.79     26.183
      85            26.619      0.09998    995    1.9624     26.423     26.816
      86            26.514      0.10001    995    1.9624     26.318      26.71
      87            26.969     0.099895    995    1.9624     26.772     27.165
      88            27.506     0.099772    995    1.9624      27.31     27.702
      89            27.394     0.099797    995    1.9624     27.198      27.59
      90            27.625     0.099746    995    1.9624     27.429      27.82
      91            28.148     0.099639    995    1.9624     27.953     28.344
      92            28.444     0.099582    995    1.9624     28.249     28.639
      93            28.688     0.099538    995    1.9624     28.493     28.884
      94            29.274     0.099441    995    1.9624     29.078     29.469
      95            29.551     0.099399    995    1.9624     29.356     29.746
      96            29.613      0.09939    995    1.9624     29.418     29.808
      97            29.774     0.099368    995    1.9624     29.579     29.969
      98            30.768     0.099248    995    1.9624     30.573     30.963
      99            30.998     0.099226    995    1.9624     30.804     31.193
     100            31.214     0.099207    995    1.9624     31.019     31.408
     101            32.519     0.099124    995    1.9624     32.325     32.714
     102            32.874     0.099113    995    1.9624     32.679     33.068
     103            32.928     0.099111    995    1.9624     32.734     33.123
     104            32.988      0.09911    995    1.9624     32.793     33.182
     105            33.344     0.099104    995    1.9624     33.149     33.538
     106            33.292     0.099105    995    1.9624     33.097     33.486
     107            33.745     0.099103    995    1.9624     33.551      33.94
     108            33.914     0.099105    995    1.9624     33.719     34.108
     109            33.792     0.099103    995    1.9624     33.598     33.987
     110            33.953     0.099105    995    1.9624     33.758     34.147
     111            34.331     0.099112    995    1.9624     34.137     34.526
     112            34.504     0.099117    995    1.9624      34.31     34.699
     113            34.545     0.099118    995    1.9624      34.35     34.739
     114            35.386      0.09916    995    1.9624     35.191      35.58
     115            35.372     0.099159    995    1.9624     35.177     35.566
     116            35.735     0.099184    995    1.9624     35.541      35.93
     117            36.524     0.099256    995    1.9624     36.329     36.719
     118            36.337     0.099237    995    1.9624     36.142     36.531
     119            36.776     0.099284    995    1.9624     36.582     36.971
     120            36.598     0.099264    995    1.9624     36.403     36.793
     121            36.863     0.099294    995    1.9624     36.668     37.058
     122            37.138     0.099328    995    1.9624     36.943     37.333
     123            37.759     0.099415    995    1.9624     37.564     37.955
     124            37.906     0.099438    995    1.9624     37.711     38.101
     125            37.936     0.099442    995    1.9624     37.741     38.131
     126            39.061     0.099644    995    1.9624     38.866     39.257
     127            39.192      0.09967    995    1.9624     38.997     39.388
     128            39.622     0.099762    995    1.9624     39.427     39.818
     129            40.121     0.099877    995    1.9624     39.925     40.317
     130            40.189     0.099893    995    1.9624     39.993     40.385
     131              40.4     0.099945    995    1.9624     40.204     40.596
     132            40.494     0.099969    995    1.9624     40.297      40.69
     133            41.147      0.10014    995    1.9624      40.95     41.343
     134            41.227      0.10017    995    1.9624     41.031     41.424
     135            41.924      0.10037    995    1.9624     41.727     42.121
     136            42.178      0.10045    995    1.9624      41.98     42.375
     137            42.333       0.1005    995    1.9624     42.136      42.53
     138            42.579      0.10058    995    1.9624     42.382     42.776
     139            42.982      0.10072    995    1.9624     42.785      43.18
     140            42.943      0.10071    995    1.9624     42.745      43.14
     141            43.667      0.10097    995    1.9624     43.469     43.866
     142            43.818      0.10103    995    1.9624      43.62     44.016
     143            44.311      0.10123    995    1.9624     44.113      44.51
     144            44.285      0.10122    995    1.9624     44.087     44.484
     145            44.692      0.10138    995    1.9624     44.494     44.891
     146            44.627      0.10136    995    1.9624     44.428     44.826
     147            45.364      0.10167    995    1.9624     45.164     45.563
     148            45.349      0.10167    995    1.9624      45.15     45.549
     149            46.555      0.10224    995    1.9624     46.354     46.755
     150            46.439      0.10218    995    1.9624     46.239      46.64
     151            46.675       0.1023    995    1.9624     46.475     46.876
     152            46.712      0.10232    995    1.9624     46.512     46.913
     153             47.46      0.10271    995    1.9624     47.258     47.661
     154            47.487      0.10272    995    1.9624     47.285     47.689
     155            48.045      0.10303    995    1.9624     47.843     48.247
     156             49.29      0.10377    995    1.9624     49.087     49.494
     157            49.509       0.1039    995    1.9624     49.305     49.713
     158            49.911      0.10416    995    1.9624     49.707     50.116
     159            50.534      0.10457    995    1.9624     50.329      50.74
     160            50.561      0.10459    995    1.9624     50.355     50.766
     161            50.745      0.10471    995    1.9624      50.54     50.951
     162            50.702      0.10468    995    1.9624     50.496     50.907
     163            50.586      0.10461    995    1.9624     50.381     50.791
     164            50.815      0.10476    995    1.9624     50.609     51.021
     165            51.675      0.10537    995    1.9624     51.468     51.882
     166             51.55      0.10528    995    1.9624     51.343     51.756
     167             51.76      0.10543    995    1.9624     51.553     51.967
     168            52.055      0.10565    995    1.9624     51.848     52.262
     169             53.97      0.10718    995    1.9624      53.76      54.18
     170            54.039      0.10724    995    1.9624     53.829      54.25
     171            54.192      0.10737    995    1.9624     53.981     54.403
     172            54.442      0.10758    995    1.9624      54.23     54.653
     173            54.227       0.1074    995    1.9624     54.016     54.438
     174             55.79       0.1088    995    1.9624     55.577     56.004
     175            57.603       0.1106    995    1.9624     57.386      57.82
     176            57.686      0.11068    995    1.9624     57.469     57.903
     177            58.061      0.11108    995    1.9624     57.843     58.279
     178            58.389      0.11143    995    1.9624      58.17     58.607
     179            59.558      0.11275    995    1.9624     59.336     59.779
     180            59.989      0.11325    995    1.9624     59.767     60.211
     181            60.367      0.11371    995    1.9624     60.144     60.591
     182            60.572      0.11396    995    1.9624     60.348     60.796
     183            60.746      0.11417    995    1.9624     60.522      60.97
     184            60.869      0.11432    995    1.9624     60.645     61.094
     185            61.028      0.11452    995    1.9624     60.803     61.253
     186            61.583      0.11522    995    1.9624     61.357     61.809
     187            61.902      0.11564    995    1.9624     61.675     62.129
     188            61.996      0.11576    995    1.9624     61.769     62.223
     189            63.154      0.11733    995    1.9624     62.924     63.385
     190            63.631      0.11801    995    1.9624     63.399     63.862
     191             63.58      0.11793    995    1.9624     63.348     63.811
     192            63.992      0.11853    995    1.9624      63.76     64.225
     193            64.172      0.11879    995    1.9624     63.939     64.405
     194             64.57      0.11938    995    1.9624     64.336     64.804
     195            64.797      0.11972    995    1.9624     64.562     65.031
     196            64.924      0.11992    995    1.9624     64.689     65.159
     197            65.624        0.121    995    1.9624     65.386     65.861
     198            65.694      0.12111    995    1.9624     65.456     65.932
     199            66.204      0.12193    995    1.9624     65.965     66.443
     200            66.256      0.12202    995    1.9624     66.017     66.496
     201            66.429       0.1223    995    1.9624     66.189     66.669
     202            67.056      0.12335    995    1.9624     66.814     67.298
     203            68.002      0.12499    995    1.9624     67.756     68.247
     204            68.373      0.12566    995    1.9624     68.127      68.62
     205            68.409      0.12572    995    1.9624     68.162     68.656
     206            68.697      0.12625    995    1.9624     68.449     68.945
     207            68.794      0.12642    995    1.9624     68.546     69.042
     208            69.029      0.12686    995    1.9624      68.78     69.278
     209            69.515      0.12778    995    1.9624     69.264     69.766
     210            69.538      0.12782    995    1.9624     69.287     69.789
     211            69.818      0.12836    995    1.9624     69.566     70.069
     212            69.792      0.12831    995    1.9624      69.54     70.043
     213            70.066      0.12885    995    1.9624     69.813     70.319
     214             70.23      0.12917    995    1.9624     69.977     70.483
     215            70.246       0.1292    995    1.9624     69.993       70.5
     216            70.584      0.12988    995    1.9624     70.329     70.839
     217            70.944      0.13061    995    1.9624     70.688     71.201
     218            71.532      0.13183    995    1.9624     71.273      71.79
     219            71.376       0.1315    995    1.9624     71.118     71.634
     220            71.209      0.13115    995    1.9624     70.951     71.466
     221            72.012      0.13285    995    1.9624     71.751     72.272
     222            71.779      0.13235    995    1.9624     71.519     72.038
     223            71.868      0.13255    995    1.9624     71.608     72.128
     224            72.136      0.13312    995    1.9624     71.875     72.397
     225             72.48      0.13388    995    1.9624     72.217     72.742
     226            73.017      0.13508    995    1.9624     72.752     73.282
     227            73.071       0.1352    995    1.9624     72.806     73.337
     228            73.165      0.13541    995    1.9624     72.899     73.431
     229            73.271      0.13566    995    1.9624     73.005     73.537
     230            73.719      0.13669    995    1.9624     73.451     73.987
     231            73.647      0.13653    995    1.9624     73.379     73.915
     232            74.187       0.1378    995    1.9624     73.917     74.458
     233            74.773      0.13923    995    1.9624       74.5     75.047
     234            74.824      0.13936    995    1.9624     74.551     75.098
     235            75.151      0.14017    995    1.9624     74.876     75.426
     236            74.784      0.13926    995    1.9624     74.511     75.058
     237            74.945      0.13966    995    1.9624     74.671     75.219
     238             75.52       0.1411    995    1.9624     75.243     75.797
     239            75.488      0.14102    995    1.9624     75.211     75.765
     240            75.537      0.14115    995    1.9624      75.26     75.814
     241            75.607      0.14133    995    1.9624     75.329     75.884
     242            76.147      0.14273    995    1.9624     75.867     76.427
     243            76.454      0.14355    995    1.9624     76.172     76.736
     244            78.286      0.14867    995    1.9624     77.995     78.578
     245            78.538      0.14941    995    1.9624     78.245     78.831
     246            79.021      0.15086    995    1.9624     78.725     79.317
     247            78.906      0.15051    995    1.9624      78.61     79.201
     248            79.872      0.15349    995    1.9624     79.571     80.174
     249            79.956      0.15376    995    1.9624     79.654     80.257
     250            80.692      0.15613    995    1.9624     80.386     80.999
     251            81.706      0.15955    995    1.9624     81.393     82.019
     252            82.542       0.1625    995    1.9624     82.223     82.861
     253            82.753      0.16326    995    1.9624     82.432     83.073
     254             82.66      0.16292    995    1.9624      82.34      82.98
     255            83.365      0.16551    995    1.9624      83.04      83.69
     256            83.487      0.16597    995    1.9624     83.161     83.812
     257            83.895      0.16752    995    1.9624     83.566     84.224
     258            84.362      0.16934    995    1.9624      84.03     84.695
     259            84.217      0.16877    995    1.9624     83.886     84.548
     260            84.413      0.16953    995    1.9624      84.08     84.746
     261            84.138      0.16846    995    1.9624     83.807     84.469
     262             84.62      0.17035    995    1.9624     84.286     84.954
     263            84.952      0.17168    995    1.9624     84.615     85.289
     264            85.074      0.17218    995    1.9624     84.736     85.412
     265            84.681       0.1706    995    1.9624     84.346     85.016
     266            85.495      0.17391    995    1.9624     85.154     85.837
     267            85.617      0.17441    995    1.9624     85.275      85.96
     268            85.792      0.17515    995    1.9624     85.449     86.136
     269            86.301      0.17731    995    1.9624     85.953     86.649
     270            86.419      0.17782    995    1.9624      86.07     86.768
     271            87.032      0.18052    995    1.9624     86.678     87.386
     272            87.531      0.18277    995    1.9624     87.172     87.889
     273            87.784      0.18393    995    1.9624     87.423     88.145
     274            87.529      0.18276    995    1.9624      87.17     87.887
     275            89.015      0.18978    995    1.9624     88.642     89.387
     276            89.302       0.1912    995    1.9624     88.927     89.677
     277             89.73      0.19334    995    1.9624      89.35     90.109
     278            89.476      0.19206    995    1.9624     89.099     89.853
     279            89.753      0.19345    995    1.9624     89.374     90.133
     280             89.89      0.19415    995    1.9624     89.509     90.271
     281            90.481       0.1972    995    1.9624     90.095     90.868
     282            90.543      0.19752    995    1.9624     90.155     90.931
     283            90.731      0.19851    995    1.9624     90.341      91.12
     284            91.115      0.20055    995    1.9624     90.722     91.509
     285            90.935      0.19959    995    1.9624     90.543     91.327
     286            91.102      0.20049    995    1.9624     90.709     91.496
     287            90.996      0.19992    995    1.9624     90.604     91.389
     288            91.479      0.20252    995    1.9624     91.082     91.877
     289            91.918      0.20494    995    1.9624     91.516      92.32
     290            91.807      0.20432    995    1.9624     91.406     92.207
     291            91.865      0.20464    995    1.9624     91.463     92.267
     292            92.155      0.20626    995    1.9624      91.75     92.559
     293            92.136      0.20615    995    1.9624     91.731      92.54
     294            92.351      0.20736    995    1.9624     91.944     92.757
     295            92.549      0.20849    995    1.9624      92.14     92.958
     296             93.21      0.21231    995    1.9624     92.794     93.627
     297            93.381      0.21331    995    1.9624     92.962     93.799
     298            93.282      0.21273    995    1.9624     92.865     93.699
     299            93.379       0.2133    995    1.9624     92.961     93.798
     300            93.357      0.21317    995    1.9624     92.939     93.775
     301            93.967       0.2168    995    1.9624     93.542     94.393
     302            94.609      0.22071    995    1.9624     94.176     95.042
     303            94.932       0.2227    995    1.9624     94.495     95.369
     304            95.023      0.22327    995    1.9624     94.585     95.461
     305            96.471      0.23252    995    1.9624     96.015     96.928
     306            96.716      0.23412    995    1.9624     96.257     97.176
     307            97.171      0.23712    995    1.9624     96.705     97.636
     308            97.286      0.23788    995    1.9624     96.819     97.752
     309            97.312      0.23805    995    1.9624     96.845     97.779
     310            97.812       0.2414    995    1.9624     97.338     98.286
     311             98.18      0.24388    995    1.9624     97.701     98.658
     312            98.376      0.24521    995    1.9624     97.895     98.858
     313            98.805      0.24813    995    1.9624     98.318     99.292
     314            99.075      0.24998    995    1.9624     98.584     99.565
     315            99.569      0.25336    995    1.9624     99.071     100.07
     316             99.43      0.25241    995    1.9624     98.935     99.925
     317            100.06      0.25671    995    1.9624     99.552     100.56
     318             99.83      0.25516    995    1.9624     99.329     100.33
     319            100.23       0.2579    995    1.9624     99.723     100.73
     320            101.12      0.26406    995    1.9624     100.61     101.64
     321            102.36      0.27242    995    1.9624     101.83      102.9
     322             102.1       0.2707    995    1.9624     101.57     102.64
     323            103.24      0.27819    995    1.9624     102.69     103.78
     324            103.15      0.27763    995    1.9624     102.61      103.7
     325            103.37      0.27904    995    1.9624     102.82     103.92
     326             103.8      0.28175    995    1.9624     103.24     104.35
     327            103.63       0.2807    995    1.9624     103.08     104.18
     328            103.52      0.27997    995    1.9624     102.97     104.07
     329            104.07      0.28345    995    1.9624     103.51     104.63
     330            103.76      0.28149    995    1.9624      103.2     104.31
     331             103.8       0.2818    995    1.9624     103.25     104.36
     332            103.99      0.28294    995    1.9624     103.43     104.54
     333            104.47      0.28592    995    1.9624     103.91     105.03
     334            104.23      0.28444    995    1.9624     103.67     104.79
     335            105.03      0.28917    995    1.9624     104.46     105.59
     336            104.82      0.28798    995    1.9624     104.26     105.39
     337            106.77      0.29833    995    1.9624     106.19     107.36
     338            106.97      0.29923    995    1.9624     106.38     107.55
     339            107.09      0.29976    995    1.9624      106.5     107.67
     340            108.75      0.30601    995    1.9624     108.15     109.35
     341            107.67      0.30224    995    1.9624     107.08     108.27
     342            108.25      0.30438    995    1.9624     107.65     108.84
     343            108.53      0.30533    995    1.9624     107.93     109.13
     344            108.56       0.3054    995    1.9624     107.96     109.16
     345            108.78      0.30608    995    1.9624     108.18     109.38
     346            109.28      0.30746    995    1.9624     108.68     109.88
     347            109.96      0.30891    995    1.9624     109.35     110.56
     348             110.7      0.30996    995    1.9624     110.09     111.31
     349             110.4       0.3096    995    1.9624     109.79        111
     350             111.8      0.31042    995    1.9624     111.19     112.41
     351            112.46      0.31006    995    1.9624     111.85     113.07
     352            112.34      0.31016    995    1.9624     111.73     112.95
     353            112.28       0.3102    995    1.9624     111.67     112.89
     354            113.23      0.30904    995    1.9624     112.63     113.84
     355            114.28      0.30669    995    1.9624     113.67     114.88
     356            113.82      0.30784    995    1.9624     113.22     114.43
     357            114.13      0.30708    995    1.9624     113.53     114.73
     358            115.04      0.30428    995    1.9624     114.45     115.64
     359            115.57      0.30232    995    1.9624     114.98     116.16
     360            115.84      0.30123    995    1.9624     115.25     116.43
     361            115.99      0.30061    995    1.9624      115.4     116.58
     362            115.83      0.30128    995    1.9624     115.23     116.42
     363             116.4      0.29878    995    1.9624     115.81     116.98
     364            116.23      0.29954    995    1.9624     115.64     116.82
     365            116.89      0.29641    995    1.9624     116.31     117.47
     366            117.28      0.29446    995    1.9624      116.7     117.85
     367            117.88       0.2912    995    1.9624     117.31     118.45
     368            119.39      0.28226    995    1.9624     118.84     119.94
     369            118.91       0.2852    995    1.9624     118.35     119.47
     370            119.75      0.28002    995    1.9624      119.2      120.3
     371            120.02      0.27828    995    1.9624     119.47     120.56
     372            120.19      0.27719    995    1.9624     119.64     120.73
     373            119.98      0.27855    995    1.9624     119.43     120.52
     374               120      0.27839    995    1.9624     119.45     120.55
     375             119.8      0.27965    995    1.9624     119.26     120.35
     376            120.81      0.27309    995    1.9624     120.27     121.35
     377            121.01      0.27179    995    1.9624     120.47     121.54
     378            121.44       0.2689    995    1.9624     120.91     121.96
     379            122.16      0.26397    995    1.9624     121.65     122.68
     380            121.74      0.26683    995    1.9624     121.22     122.27
     381            122.45      0.26202    995    1.9624     121.94     122.96
     382            121.91      0.26571    995    1.9624     121.39     122.43
     383            122.16      0.26402    995    1.9624     121.64     122.67
     384            122.57      0.26119    995    1.9624     122.06     123.08
     385            122.55      0.26134    995    1.9624     122.04     123.06
     386            122.83      0.25944    995    1.9624     122.32     123.33
     387            122.88      0.25907    995    1.9624     122.37     123.39
     388            123.46       0.2551    995    1.9624     122.96     123.96
     389            123.27       0.2564    995    1.9624     122.77     123.77
     390            123.69      0.25354    995    1.9624     123.19     124.18
     391            123.93      0.25188    995    1.9624     123.44     124.42
     392            124.63      0.24711    995    1.9624     124.15     125.12
     393            125.02      0.24446    995    1.9624     124.54      125.5
     394            124.92      0.24512    995    1.9624     124.44     125.41
     395            125.57      0.24078    995    1.9624      125.1     126.05
     396            125.45      0.24163    995    1.9624     124.97     125.92
     397            126.17      0.23685    995    1.9624      125.7     126.63
     398            126.31      0.23592    995    1.9624     125.84     126.77
     399            125.96      0.23822    995    1.9624     125.49     126.43
     400            126.18      0.23676    995    1.9624     125.71     126.64
     401            127.14      0.23053    995    1.9624     126.69     127.59
     402            127.53        0.228    995    1.9624     127.09     127.98
     403            126.73      0.23314    995    1.9624     126.28     127.19
     404            127.07      0.23097    995    1.9624     126.62     127.52
     405            127.42      0.22875    995    1.9624     126.97     127.87
     406            127.74      0.22667    995    1.9624      127.3     128.19
     407            127.92      0.22557    995    1.9624     127.48     128.36
     408            128.22      0.22369    995    1.9624     127.78     128.66
     409             128.5      0.22196    995    1.9624     128.07     128.94
     410            129.15        0.218    995    1.9624     128.73     129.58
     411            129.01      0.21887    995    1.9624     128.58     129.44
     412            129.14      0.21808    995    1.9624     128.71     129.57
     413            129.56      0.21558    995    1.9624     129.14     129.98
     414            129.45      0.21624    995    1.9624     129.02     129.87
     415            129.34      0.21687    995    1.9624     128.92     129.77
     416            129.55      0.21567    995    1.9624     129.12     129.97
     417            130.04      0.21279    995    1.9624     129.62     130.45
     418            131.32      0.20555    995    1.9624     130.91     131.72
     419             130.9      0.20788    995    1.9624     130.49     131.31
     420            130.56      0.20977    995    1.9624     130.15     130.97
     421            131.72      0.20335    995    1.9624     131.32     132.12
     422            131.98      0.20197    995    1.9624     131.58     132.37
     423            132.17      0.20094    995    1.9624     131.78     132.56
     424            132.33      0.20011    995    1.9624     131.93     132.72
     425            132.76      0.19787    995    1.9624     132.37     133.14
     426            133.16       0.1958    995    1.9624     132.78     133.54
     427            133.18      0.19571    995    1.9624     132.79     133.56
     428            133.61      0.19352    995    1.9624     133.23     133.99
     429            133.88      0.19219    995    1.9624     133.51     134.26
     430            134.05      0.19135    995    1.9624     133.68     134.43
     431            134.96      0.18701    995    1.9624      134.6     135.33
     432            134.97      0.18695    995    1.9624     134.61     135.34
     433            135.16      0.18611    995    1.9624     134.79     135.52
     434            135.33      0.18532    995    1.9624     134.96     135.69
     435            135.51      0.18449    995    1.9624     135.15     135.87
     436            135.55       0.1843    995    1.9624     135.19     135.91
     437            136.02       0.1822    995    1.9624     135.66     136.37
     438            135.62        0.184    995    1.9624     135.26     135.98
     439            136.16      0.18158    995    1.9624      135.8     136.51
     440            135.99      0.18233    995    1.9624     135.63     136.35
     441            136.26      0.18115    995    1.9624      135.9     136.61
     442             136.7      0.17921    995    1.9624     136.35     137.05
     443            136.27      0.18106    995    1.9624     135.92     136.63
     444            137.22        0.177    995    1.9624     136.87     137.57
     445            137.27      0.17678    995    1.9624     136.93     137.62
     446            137.39       0.1763    995    1.9624     137.04     137.73
     447            138.04      0.17363    995    1.9624      137.7     138.38
     448            137.73      0.17491    995    1.9624     137.38     138.07
     449            137.85      0.17441    995    1.9624     137.51     138.19
     450             138.5      0.17179    995    1.9624     138.16     138.84
     451            137.87      0.17433    995    1.9624     137.53     138.21
     452            138.73       0.1709    995    1.9624     138.39     139.06
     453            139.07      0.16959    995    1.9624     138.73      139.4
     454            139.56      0.16773    995    1.9624     139.23     139.89
     455            139.48      0.16803    995    1.9624     139.15     139.81
     456             139.4      0.16833    995    1.9624     139.07     139.73
     457            140.68      0.16363    995    1.9624     140.36     141.01
     458            141.22      0.16175    995    1.9624      140.9     141.54
     459            141.14      0.16202    995    1.9624     140.83     141.46
     460            141.33      0.16138    995    1.9624     141.01     141.64
     461            141.49      0.16083    995    1.9624     141.17      141.8
     462            142.42      0.15772    995    1.9624     142.11     142.73
     463            142.62      0.15709    995    1.9624     142.31     142.93
     464            143.51      0.15429    995    1.9624      143.2     143.81
     465            143.61      0.15396    995    1.9624     143.31     143.92
     466            143.54      0.15418    995    1.9624     143.24     143.84
     467            144.55      0.15116    995    1.9624     144.25     144.84
     468             144.9      0.15013    995    1.9624     144.61      145.2
     469            145.14      0.14943    995    1.9624     144.85     145.44
     470             145.4      0.14871    995    1.9624     145.11     145.69
     471            145.59      0.14818    995    1.9624      145.3     145.88
     472            146.06      0.14688    995    1.9624     145.77     146.35
     473            146.45      0.14583    995    1.9624     146.16     146.74
     474            147.13      0.14402    995    1.9624     146.85     147.42
     475            147.17      0.14394    995    1.9624     146.89     147.45
     476            147.45      0.14321    995    1.9624     147.17     147.73
     477            147.48      0.14315    995    1.9624      147.2     147.76
     478            147.29      0.14361    995    1.9624     147.01     147.58
     479            148.28      0.14114    995    1.9624        148     148.56
     480            148.25      0.14121    995    1.9624     147.98     148.53
     481            148.28      0.14113    995    1.9624     148.01     148.56
     482            149.71      0.13777    995    1.9624     149.44     149.98
     483            150.98      0.13494    995    1.9624     150.72     151.24
     484            151.65      0.13352    995    1.9624     151.39     151.91
     485             152.9      0.13099    995    1.9624     152.64     153.16
     486            152.99      0.13081    995    1.9624     152.74     153.25
     487            153.24      0.13032    995    1.9624     152.99      153.5
     488             153.8      0.12927    995    1.9624     153.54     154.05
     489            154.15       0.1286    995    1.9624      153.9     154.41
     490            155.69      0.12585    995    1.9624     155.44     155.94
     491            155.92      0.12546    995    1.9624     155.67     156.16
     492               156      0.12533    995    1.9624     155.75     156.24
     493            156.01       0.1253    995    1.9624     155.76     156.26
     494            156.03      0.12527    995    1.9624     155.78     156.28
     495            156.01       0.1253    995    1.9624     155.77     156.26
     496            156.24      0.12492    995    1.9624     155.99     156.48
     497            156.53      0.12444    995    1.9624     156.28     156.77
     498            156.73       0.1241    995    1.9624     156.49     156.98
     499            156.61       0.1243    995    1.9624     156.36     156.85
     500            156.77      0.12404    995    1.9624     156.53     157.01
     501             157.4      0.12302    995    1.9624     157.16     157.65
     502            157.88      0.12227    995    1.9624     157.64     158.12
     503           -158.25      0.12146    995    1.9624    -158.48    -158.01
     504           -157.81      0.12081    995    1.9624    -158.05    -157.58
     505           -157.09      0.11976    995    1.9624    -157.33    -156.86
     506           -156.92      0.11952    995    1.9624    -157.16    -156.69
     507            -156.6      0.11907    995    1.9624    -156.84    -156.37
     508           -156.69      0.11919    995    1.9624    -156.93    -156.46
     509           -155.08      0.11701    995    1.9624    -155.31    -154.85
     510           -154.86      0.11672    995    1.9624    -155.09    -154.63
     511           -154.83      0.11669    995    1.9624    -155.06     -154.6
     512           -154.47      0.11623    995    1.9624     -154.7    -154.24
     513           -154.35      0.11607    995    1.9624    -154.58    -154.12
     514           -154.06      0.11571    995    1.9624    -154.29    -153.83
     515           -153.62      0.11517    995    1.9624    -153.84    -153.39
     516           -153.58      0.11512    995    1.9624     -153.8    -153.35
     517           -153.45      0.11496    995    1.9624    -153.67    -153.22
     518           -153.29      0.11477    995    1.9624    -153.51    -153.06
     519           -153.21      0.11468    995    1.9624    -153.44    -152.99
     520           -153.03      0.11446    995    1.9624    -153.25     -152.8
     521            -153.1      0.11454    995    1.9624    -153.32    -152.87
     522           -152.23      0.11354    995    1.9624    -152.45    -152.01
     523           -152.12      0.11341    995    1.9624    -152.34     -151.9
     524           -151.64      0.11288    995    1.9624    -151.87    -151.42
     525           -151.44      0.11266    995    1.9624    -151.67    -151.22
     526           -150.72      0.11188    995    1.9624    -150.94     -150.5
     527           -150.78      0.11194    995    1.9624       -151    -150.56
     528           -150.55      0.11171    995    1.9624    -150.77    -150.33
     529           -150.38      0.11153    995    1.9624     -150.6    -150.16
     530           -150.05      0.11119    995    1.9624    -150.27    -149.83
     531            -149.9      0.11104    995    1.9624    -150.12    -149.68
     532            -149.4      0.11053    995    1.9624    -149.61    -149.18
     533           -149.33      0.11047    995    1.9624    -149.55    -149.12
     534           -149.07      0.11022    995    1.9624    -149.29    -148.85
     535           -148.61      0.10978    995    1.9624    -148.83     -148.4
     536           -147.94      0.10916    995    1.9624    -148.16    -147.73
     537           -147.96      0.10918    995    1.9624    -148.18    -147.75
     538           -146.81      0.10815    995    1.9624    -147.02     -146.6
     539           -146.59      0.10797    995    1.9624     -146.8    -146.38
     540           -146.46      0.10786    995    1.9624    -146.68    -146.25
     541           -146.53      0.10792    995    1.9624    -146.74    -146.32
     542            -145.4      0.10699    995    1.9624    -145.61    -145.19
     543           -144.78       0.1065    995    1.9624    -144.99    -144.57
     544           -144.02      0.10593    995    1.9624    -144.22    -143.81
     545           -143.88      0.10583    995    1.9624    -144.09    -143.67
     546           -143.46      0.10553    995    1.9624    -143.67    -143.26
     547           -143.51      0.10557    995    1.9624    -143.72    -143.31
     548           -143.36      0.10546    995    1.9624    -143.57    -143.15
     549           -143.36      0.10546    995    1.9624    -143.57    -143.15
     550           -143.31      0.10542    995    1.9624    -143.52     -143.1
     551           -143.01      0.10522    995    1.9624    -143.22     -142.8
     552           -142.21      0.10468    995    1.9624    -142.41       -142
     553           -141.98      0.10453    995    1.9624    -142.19    -141.78
     554           -142.05      0.10458    995    1.9624    -142.26    -141.85
     555           -141.59      0.10428    995    1.9624     -141.8    -141.39
     556           -141.06      0.10395    995    1.9624    -141.27    -140.86
     557           -140.76      0.10377    995    1.9624    -140.97    -140.56
     558           -140.81       0.1038    995    1.9624    -141.02    -140.61
     559           -140.06      0.10336    995    1.9624    -140.26    -139.85
     560           -139.07      0.10282    995    1.9624    -139.27    -138.87
     561           -138.91      0.10274    995    1.9624    -139.12    -138.71
     562           -138.99      0.10278    995    1.9624     -139.2    -138.79
     563           -138.85       0.1027    995    1.9624    -139.05    -138.65
     564           -138.66       0.1026    995    1.9624    -138.86    -138.46
     565           -138.13      0.10234    995    1.9624    -138.34    -137.93
     566           -137.76      0.10216    995    1.9624    -137.96    -137.56
     567           -137.61      0.10208    995    1.9624    -137.81    -137.41
     568           -137.32      0.10195    995    1.9624    -137.52    -137.12
     569           -137.22       0.1019    995    1.9624    -137.42    -137.02
     570           -136.51      0.10159    995    1.9624    -136.71    -136.31
     571           -136.43      0.10156    995    1.9624    -136.63    -136.24
     572           -135.79      0.10129    995    1.9624    -135.98    -135.59
     573           -135.59      0.10121    995    1.9624    -135.79    -135.39
     574           -134.87      0.10093    995    1.9624    -135.06    -134.67
     575           -134.65      0.10085    995    1.9624    -134.85    -134.45
     576           -134.83      0.10092    995    1.9624    -135.03    -134.64
     577           -133.62       0.1005    995    1.9624    -133.82    -133.42
     578           -133.35      0.10041    995    1.9624    -133.55    -133.15
     579           -132.95      0.10029    995    1.9624    -133.15    -132.76
     580           -132.71      0.10022    995    1.9624     -132.9    -132.51
     581           -132.62      0.10019    995    1.9624    -132.82    -132.42
     582           -130.74     0.099716    995    1.9624    -130.93    -130.54
     583           -129.44     0.099462    995    1.9624    -129.63    -129.24
     584           -129.13      0.09941    995    1.9624    -129.32    -128.93
     585           -128.81     0.099361    995    1.9624    -129.01    -128.62
     586           -126.97     0.099146    995    1.9624    -127.16    -126.77
     587           -127.06     0.099154    995    1.9624    -127.26    -126.87
     588           -126.94     0.099144    995    1.9624    -127.13    -126.74
     589           -126.65     0.099122    995    1.9624    -126.85    -126.46
     590           -126.17     0.099091    995    1.9624    -126.36    -125.97
     591           -126.03     0.099084    995    1.9624    -126.22    -125.83
     592           -125.94      0.09908    995    1.9624    -126.14    -125.75
     593           -125.42     0.099061    995    1.9624    -125.62    -125.23
     594           -125.22     0.099056    995    1.9624    -125.41    -125.02
     595           -125.24     0.099056    995    1.9624    -125.44    -125.05
     596           -125.04     0.099053    995    1.9624    -125.23    -124.84
     597           -124.79      0.09905    995    1.9624    -124.98    -124.59
     598           -123.83     0.099063    995    1.9624    -124.02    -123.64
     599           -123.82     0.099063    995    1.9624    -124.01    -123.62
     600           -123.69     0.099067    995    1.9624    -123.89     -123.5
     601            -123.6      0.09907    995    1.9624     -123.8    -123.41
     602           -123.07     0.099096    995    1.9624    -123.26    -122.88
     603           -122.88     0.099108    995    1.9624    -123.07    -122.68
     604           -122.75     0.099116    995    1.9624    -122.95    -122.56
     605           -122.44     0.099139    995    1.9624    -122.64    -122.25
     606           -121.83     0.099196    995    1.9624    -122.03    -121.64
     607           -121.47     0.099236    995    1.9624    -121.66    -121.27
     608           -121.31     0.099255    995    1.9624     -121.5    -121.11
     609           -120.98     0.099298    995    1.9624    -121.17    -120.78
     610           -120.83     0.099318    995    1.9624    -121.03    -120.64
     611           -120.69     0.099338    995    1.9624    -120.88    -120.49
     612           -119.65      0.09951    995    1.9624    -119.85    -119.46
     613           -119.42     0.099555    995    1.9624    -119.61    -119.22
     614           -119.27     0.099584    995    1.9624    -119.46    -119.07
     615           -119.27     0.099582    995    1.9624    -119.47    -119.08
     616           -119.14     0.099609    995    1.9624    -119.34    -118.95
     617              -119     0.099639    995    1.9624    -119.19     -118.8
     618              -119     0.099637    995    1.9624     -119.2    -118.81
     619           -118.39     0.099772    995    1.9624    -118.59     -118.2
     620           -118.34     0.099784    995    1.9624    -118.54    -118.15
     621           -118.15     0.099831    995    1.9624    -118.34    -117.95
     622           -117.86     0.099901    995    1.9624    -118.06    -117.67
     623           -117.74     0.099933    995    1.9624    -117.94    -117.54
     624           -117.82     0.099913    995    1.9624    -118.01    -117.62
     625           -117.06      0.10012    995    1.9624    -117.26    -116.87
     626           -117.04      0.10012    995    1.9624    -117.24    -116.85
     627           -116.95      0.10015    995    1.9624    -117.15    -116.76
     628           -116.52      0.10028    995    1.9624    -116.72    -116.32
     629           -116.33      0.10034    995    1.9624    -116.52    -116.13
     630           -116.35      0.10033    995    1.9624    -116.55    -116.15
     631            -116.4      0.10031    995    1.9624     -116.6     -116.2
     632           -116.37      0.10032    995    1.9624    -116.57    -116.18
     633           -116.12       0.1004    995    1.9624    -116.31    -115.92
     634           -115.07      0.10076    995    1.9624    -115.27    -114.87
     635           -115.05      0.10077    995    1.9624    -115.25    -114.85
     636            -113.6      0.10134    995    1.9624     -113.8     -113.4
     637           -113.43      0.10141    995    1.9624    -113.62    -113.23
     638           -112.83      0.10167    995    1.9624    -113.03    -112.64
     639           -112.09      0.10203    995    1.9624    -112.29    -111.89
     640           -112.07      0.10203    995    1.9624    -112.27    -111.87
     641           -111.75      0.10219    995    1.9624    -111.95    -111.55
     642           -111.41      0.10236    995    1.9624    -111.61    -111.21
     643           -111.62      0.10226    995    1.9624    -111.82    -111.42
     644           -111.39      0.10237    995    1.9624    -111.59    -111.19
     645           -111.34       0.1024    995    1.9624    -111.54    -111.14
     646           -111.23      0.10246    995    1.9624    -111.43    -111.03
     647           -110.83      0.10267    995    1.9624    -111.03    -110.63
     648           -110.27      0.10298    995    1.9624    -110.47    -110.07
     649           -109.53      0.10341    995    1.9624    -109.73    -109.33
     650           -108.89      0.10381    995    1.9624    -109.09    -108.68
     651           -108.64      0.10396    995    1.9624    -108.84    -108.43
     652           -108.44      0.10409    995    1.9624    -108.64    -108.23
     653           -108.47      0.10407    995    1.9624    -108.68    -108.27
     654           -107.97       0.1044    995    1.9624    -108.17    -107.76
     655           -108.21      0.10424    995    1.9624    -108.41       -108
     656           -107.93      0.10443    995    1.9624    -108.13    -107.72
     657           -107.24       0.1049    995    1.9624    -107.45    -107.04
     658              -107      0.10507    995    1.9624     -107.2    -106.79
     659           -106.51      0.10543    995    1.9624    -106.71     -106.3
     660           -106.52      0.10542    995    1.9624    -106.72    -106.31
     661           -105.92      0.10587    995    1.9624    -106.13    -105.71
     662           -105.25       0.1064    995    1.9624    -105.46    -105.04
     663           -105.04      0.10656    995    1.9624    -105.25    -104.83
     664           -105.05      0.10656    995    1.9624    -105.26    -104.84
     665           -104.87      0.10671    995    1.9624    -105.08    -104.66
     666            -104.6      0.10693    995    1.9624    -104.81    -104.39
     667           -104.77      0.10678    995    1.9624    -104.98    -104.56
     668           -103.01      0.10832    995    1.9624    -103.23     -102.8
     669           -102.08      0.10919    995    1.9624     -102.3    -101.87
     670           -101.91      0.10936    995    1.9624    -102.13     -101.7
     671           -101.95      0.10932    995    1.9624    -102.16    -101.73
     672           -101.75      0.10952    995    1.9624    -101.97    -101.54
     673           -101.37      0.10989    995    1.9624    -101.59    -101.16
     674           -100.41      0.11089    995    1.9624    -100.62    -100.19
     675           -99.565      0.11181    995    1.9624    -99.785    -99.346
     676            -99.29      0.11212    995    1.9624     -99.51     -99.07
     677           -99.322      0.11208    995    1.9624    -99.542    -99.102
     678           -98.406      0.11314    995    1.9624    -98.628    -98.184
     679           -98.535      0.11299    995    1.9624    -98.757    -98.313
     680           -98.364      0.11319    995    1.9624    -98.586    -98.142
     681           -98.224      0.11335    995    1.9624    -98.446    -98.002
     682           -98.075      0.11353    995    1.9624    -98.298    -97.852
     683           -97.821      0.11384    995    1.9624    -98.044    -97.597
     684           -97.201      0.11461    995    1.9624    -97.426    -96.976
     685           -96.817       0.1151    995    1.9624    -97.043    -96.592
     686           -96.538      0.11546    995    1.9624    -96.765    -96.311
     687           -96.608      0.11537    995    1.9624    -96.835    -96.382
     688           -96.312      0.11575    995    1.9624     -96.54    -96.085
     689           -95.922      0.11627    995    1.9624    -96.151    -95.694
     690           -96.066      0.11608    995    1.9624    -96.293    -95.838
     691           -95.532       0.1168    995    1.9624    -95.762    -95.303
     692           -95.374      0.11702    995    1.9624    -95.604    -95.144
     693           -95.348      0.11706    995    1.9624    -95.578    -95.118
     694            -95.15      0.11733    995    1.9624     -95.38     -94.92
     695           -94.907      0.11768    995    1.9624    -95.138    -94.676
     696           -94.373      0.11844    995    1.9624    -94.605    -94.141
     697           -94.345      0.11848    995    1.9624    -94.577    -94.112
     698           -94.329      0.11851    995    1.9624    -94.562    -94.097
     699           -93.543      0.11968    995    1.9624    -93.778    -93.308
     700           -93.468      0.11979    995    1.9624    -93.703    -93.233
     701           -93.248      0.12013    995    1.9624    -93.483    -93.012
     702           -93.025      0.12047    995    1.9624    -93.261    -92.789
     703           -93.269      0.12009    995    1.9624    -93.505    -93.034
     704            -92.57      0.12119    995    1.9624    -92.808    -92.332
     705           -91.938      0.12221    995    1.9624    -92.178    -91.698
     706           -91.892      0.12228    995    1.9624    -92.131    -91.652
     707           -91.687      0.12262    995    1.9624    -91.928    -91.447
     708           -91.681      0.12263    995    1.9624    -91.922     -91.44
     709           -91.689      0.12262    995    1.9624    -91.929    -91.448
     710           -90.971      0.12383    995    1.9624    -91.214    -90.728
     711           -91.126      0.12357    995    1.9624    -91.368    -90.883
     712           -90.829      0.12408    995    1.9624    -91.072    -90.585
     713           -90.526      0.12461    995    1.9624     -90.77    -90.281
     714           -89.263       0.1269    995    1.9624    -89.512    -89.014
     715           -89.456      0.12654    995    1.9624    -89.705    -89.208
     716           -89.378      0.12668    995    1.9624    -89.627     -89.13
     717           -89.314       0.1268    995    1.9624    -89.562    -89.065
     718           -89.361      0.12672    995    1.9624     -89.61    -89.112
     719           -88.847      0.12769    995    1.9624    -89.097    -88.596
     720           -88.724      0.12792    995    1.9624    -88.975    -88.473
     721           -88.172      0.12899    995    1.9624    -88.426    -87.919
     722           -87.911      0.12951    995    1.9624    -88.165    -87.657
     723           -87.131       0.1311    995    1.9624    -87.388    -86.874
     724           -86.844       0.1317    995    1.9624    -87.102    -86.586
     725           -86.804      0.13178    995    1.9624    -87.062    -86.545
     726            -86.65      0.13211    995    1.9624    -86.909    -86.391
     727           -86.544      0.13233    995    1.9624    -86.804    -86.285
     728           -86.238      0.13299    995    1.9624    -86.499    -85.977
     729               -85      0.13575    995    1.9624    -85.267    -84.734
     730           -84.908      0.13597    995    1.9624    -85.175    -84.641
     731           -84.336      0.13731    995    1.9624    -84.605    -84.066
     732           -84.353      0.13726    995    1.9624    -84.622    -84.084
     733           -83.972      0.13818    995    1.9624    -84.243    -83.701
     734           -83.392       0.1396    995    1.9624    -83.666    -83.118
     735           -83.431       0.1395    995    1.9624    -83.705    -83.157
     736           -83.429      0.13951    995    1.9624    -83.702    -83.155
     737           -82.787      0.14112    995    1.9624    -83.064     -82.51
     738           -82.961      0.14068    995    1.9624    -83.237    -82.684
     739           -83.025      0.14052    995    1.9624    -83.301    -82.749
     740           -82.954       0.1407    995    1.9624     -83.23    -82.678
     741           -83.072       0.1404    995    1.9624    -83.347    -82.796
     742           -82.827      0.14102    995    1.9624    -83.104     -82.55
     743           -82.334      0.14229    995    1.9624    -82.613    -82.055
     744           -81.915       0.1434    995    1.9624    -82.196    -81.633
     745           -81.784      0.14375    995    1.9624    -82.066    -81.502
     746            -81.65      0.14411    995    1.9624    -81.933    -81.367
     747           -80.814      0.14642    995    1.9624    -81.101    -80.527
     748           -80.561      0.14713    995    1.9624     -80.85    -80.273
     749           -79.294      0.15085    995    1.9624     -79.59    -78.998
     750           -79.236      0.15103    995    1.9624    -79.532    -78.939
     751           -78.797      0.15238    995    1.9624    -79.096    -78.498
     752           -78.447      0.15347    995    1.9624    -78.748    -78.146
     753           -78.597        0.153    995    1.9624    -78.898    -78.297
     754           -78.066      0.15469    995    1.9624    -78.369    -77.762
     755           -77.625      0.15612    995    1.9624    -77.931    -77.319
     756           -77.223      0.15745    995    1.9624    -77.532    -76.914
     757           -77.253      0.15735    995    1.9624    -77.562    -76.944
     758           -76.643      0.15942    995    1.9624    -76.956     -76.33
     759            -76.66      0.15937    995    1.9624    -76.972    -76.347
     760           -76.471      0.16002    995    1.9624    -76.785    -76.157
     761           -76.559      0.15971    995    1.9624    -76.873    -76.246
     762            -75.86      0.16217    995    1.9624    -76.178    -75.542
     763           -74.207      0.16833    995    1.9624    -74.537    -73.877
     764           -74.041      0.16898    995    1.9624    -74.373     -73.71
     765           -74.205      0.16834    995    1.9624    -74.535    -73.874
     766           -74.078      0.16884    995    1.9624    -74.409    -73.746
     767           -74.012      0.16909    995    1.9624    -74.344     -73.68
     768            -73.72      0.17024    995    1.9624    -74.054    -73.386
     769           -73.284      0.17199    995    1.9624    -73.621    -72.946
     770           -72.834      0.17384    995    1.9624    -73.175    -72.493
     771            -72.61      0.17477    995    1.9624    -72.953    -72.267
     772           -72.621      0.17472    995    1.9624    -72.964    -72.278
     773           -72.132      0.17679    995    1.9624    -72.479    -71.785
     774           -71.946       0.1776    995    1.9624    -72.294    -71.597
     775           -71.579      0.17919    995    1.9624    -71.931    -71.227
     776           -70.889      0.18228    995    1.9624    -71.247    -70.531
     777            -70.86      0.18241    995    1.9624    -71.218    -70.502
     778           -70.865      0.18239    995    1.9624    -71.223    -70.507
     779           -70.307      0.18496    995    1.9624     -70.67    -69.944
     780            -70.69      0.18319    995    1.9624    -71.049     -70.33
     781           -69.943      0.18667    995    1.9624    -70.309    -69.577
     782           -69.645       0.1881    995    1.9624    -70.014    -69.276
     783           -69.493      0.18883    995    1.9624    -69.864    -69.123
     784           -69.681      0.18792    995    1.9624     -70.05    -69.312
     785           -69.505      0.18878    995    1.9624    -69.875    -69.134
     786           -68.616      0.19317    995    1.9624    -68.995    -68.237
     787            -67.99      0.19637    995    1.9624    -68.375    -67.605
     788           -67.957      0.19655    995    1.9624    -68.342    -67.571
     789           -67.877      0.19696    995    1.9624    -68.263     -67.49
     790           -67.693      0.19792    995    1.9624    -68.081    -67.304
     791           -67.248      0.20029    995    1.9624    -67.641    -66.855
     792           -67.281      0.20011    995    1.9624    -67.674    -66.889
     793           -67.073      0.20123    995    1.9624    -67.467    -66.678
     794           -66.995      0.20165    995    1.9624     -67.39    -66.599
     795           -66.908      0.20212    995    1.9624    -67.304    -66.511
     796           -66.872      0.20232    995    1.9624    -67.269    -66.475
     797           -66.438       0.2047    995    1.9624     -66.84    -66.037
     798           -65.878      0.20785    995    1.9624    -66.286     -65.47
     799           -66.056      0.20684    995    1.9624    -66.462     -65.65
     800           -65.711      0.20879    995    1.9624    -66.121    -65.302
     801           -64.632      0.21509    995    1.9624    -65.054     -64.21
     802           -63.611      0.22129    995    1.9624    -64.045    -63.177
     803           -63.654      0.22102    995    1.9624    -64.088     -63.22
     804           -63.093      0.22452    995    1.9624    -63.533    -62.652
     805           -62.511      0.22821    995    1.9624    -62.959    -62.063
     806           -62.621       0.2275    995    1.9624    -63.068    -62.175
     807           -62.714      0.22692    995    1.9624    -63.159    -62.268
     808           -61.943      0.23187    995    1.9624    -62.398    -61.488
     809            -61.88      0.23228    995    1.9624    -62.336    -61.424
     810           -61.241      0.23648    995    1.9624    -61.706    -60.777
     811           -60.587      0.24084    995    1.9624    -61.059    -60.114
     812           -60.476      0.24159    995    1.9624     -60.95    -60.002
     813           -60.225      0.24328    995    1.9624    -60.702    -59.747
     814           -60.594      0.24079    995    1.9624    -61.067    -60.122
     815           -59.851      0.24582    995    1.9624    -60.333    -59.368
     816           -59.544      0.24791    995    1.9624    -60.031    -59.058
     817           -59.585      0.24763    995    1.9624    -60.071    -59.099
     818           -59.203      0.25024    995    1.9624    -59.694    -58.712
     819           -59.327      0.24939    995    1.9624    -59.817    -58.838
     820           -58.802      0.25299    995    1.9624    -59.298    -58.305
     821           -58.919      0.25219    995    1.9624    -59.414    -58.424
     822           -58.794      0.25305    995    1.9624     -59.29    -58.297
     823           -58.917       0.2522    995    1.9624    -59.412    -58.422
     824           -58.614      0.25428    995    1.9624    -59.113    -58.115
     825           -57.945      0.25889    995    1.9624    -58.453    -57.437
     826           -57.929        0.259    995    1.9624    -58.437    -57.421
     827           -58.006      0.25847    995    1.9624    -58.513    -57.498
     828            -57.46      0.26223    995    1.9624    -57.974    -56.945
     829           -56.007      0.27209    995    1.9624    -56.541    -55.473
     830           -56.047      0.27183    995    1.9624     -56.58    -55.513
     831            -56.34      0.26985    995    1.9624     -56.87    -55.811
     832           -56.825      0.26656    995    1.9624    -57.349    -56.302
     833           -56.063      0.27172    995    1.9624    -56.596     -55.53
     834           -55.806      0.27343    995    1.9624    -56.342    -55.269
     835           -55.853      0.27312    995    1.9624    -56.388    -55.317
     836           -54.782      0.28011    995    1.9624    -55.331    -54.232
     837           -54.857      0.27963    995    1.9624    -55.406    -54.309
     838           -54.805      0.27996    995    1.9624    -55.354    -54.256
     839           -54.533      0.28168    995    1.9624    -55.086     -53.98
     840           -54.222      0.28362    995    1.9624    -54.779    -53.666
     841           -54.176      0.28391    995    1.9624    -54.733    -53.618
     842           -53.482      0.28808    995    1.9624    -54.047    -52.917
     843           -53.309      0.28909    995    1.9624    -53.876    -52.741
     844            -53.35      0.28885    995    1.9624    -53.917    -52.783
     845           -53.385      0.28864    995    1.9624    -53.952    -52.819
     846           -52.925      0.29126    995    1.9624    -53.496    -52.353
     847           -53.176      0.28985    995    1.9624    -53.744    -52.607
     848           -53.027      0.29069    995    1.9624    -53.597    -52.456
     849           -52.886      0.29147    995    1.9624    -53.458    -52.314
     850           -52.241      0.29493    995    1.9624     -52.82    -51.662
     851           -52.232      0.29498    995    1.9624    -52.811    -51.653
     852           -51.616      0.29802    995    1.9624    -52.201    -51.031
     853           -51.202      0.29991    995    1.9624     -51.79    -50.613
     854           -51.398      0.29903    995    1.9624    -51.985    -50.811
     855           -51.492       0.2986    995    1.9624    -52.078    -50.906
     856           -50.351      0.30338    995    1.9624    -50.947    -49.756
     857           -49.996      0.30464    995    1.9624    -50.594    -49.398
     858           -50.288      0.30361    995    1.9624    -50.884    -49.692
     859           -49.415      0.30646    995    1.9624    -50.017    -48.814
     860            -49.66      0.30573    995    1.9624     -50.26     -49.06
     861           -49.382      0.30656    995    1.9624    -49.983     -48.78
     862           -48.709      0.30823    995    1.9624    -49.313    -48.104
     863           -48.147      0.30928    995    1.9624    -48.754     -47.54
     864           -47.653      0.30993    995    1.9624    -48.261    -47.045
     865           -47.077      0.31035    995    1.9624    -47.686    -46.468
     866           -46.381      0.31038    995    1.9624     -46.99    -45.772
     867           -45.608      0.30979    995    1.9624    -46.216    -45.001
     868           -45.682      0.30987    995    1.9624     -46.29    -45.074
     869           -45.195      0.30921    995    1.9624    -45.802    -44.589
     870           -44.891      0.30868    995    1.9624    -45.497    -44.285
     871           -45.469      0.30962    995    1.9624    -46.077    -44.862
     872           -44.779      0.30845    995    1.9624    -45.384    -44.174
     873           -44.807      0.30851    995    1.9624    -45.412    -44.201
     874           -43.961      0.30644    995    1.9624    -44.562     -43.36
     875           -44.519      0.30789    995    1.9624    -45.123    -43.915
     876           -44.027      0.30663    995    1.9624    -44.628    -43.425
     877           -44.635      0.30815    995    1.9624    -45.239     -44.03
     878           -43.805      0.30599    995    1.9624    -44.406    -43.205
     879           -43.418      0.30475    995    1.9624    -44.016     -42.82
     880           -43.095      0.30362    995    1.9624    -43.691      -42.5
     881           -42.138      0.29974    995    1.9624    -42.727     -41.55
     882           -41.313      0.29582    995    1.9624    -41.893    -40.732
     883           -40.932      0.29386    995    1.9624    -41.509    -40.355
     884           -40.236      0.29005    995    1.9624    -40.805    -39.667
     885           -39.565      0.28614    995    1.9624    -40.127    -39.004
     886           -39.422      0.28527    995    1.9624    -39.982    -38.862
     887           -39.446      0.28542    995    1.9624    -40.006    -38.885
     888           -39.753      0.28725    995    1.9624    -40.317     -39.19
     889           -39.301      0.28454    995    1.9624     -39.86    -38.743
     890           -39.351      0.28484    995    1.9624     -39.91    -38.792
     891           -38.676      0.28065    995    1.9624    -39.227    -38.125
     892           -38.743      0.28107    995    1.9624    -39.294    -38.191
     893           -38.722      0.28094    995    1.9624    -39.273    -38.171
     894            -38.33      0.27845    995    1.9624    -38.877    -37.784
     895           -37.871      0.27546    995    1.9624    -38.412     -37.33
     896           -37.271      0.27149    995    1.9624    -37.804    -36.738
     897           -37.414      0.27244    995    1.9624    -37.949    -36.879
     898            -37.56      0.27342    995    1.9624    -38.097    -37.024
     899           -37.259      0.27141    995    1.9624    -37.791    -36.726
     900           -37.159      0.27074    995    1.9624     -37.69    -36.628
     901           -36.901      0.26901    995    1.9624    -37.429    -36.373
     902           -36.684      0.26754    995    1.9624    -37.209    -36.159
     903           -36.343      0.26523    995    1.9624    -36.863    -35.822
     904           -35.922      0.26236    995    1.9624    -36.437    -35.407
     905           -36.221       0.2644    995    1.9624     -36.74    -35.702
     906           -35.092      0.25668    995    1.9624    -35.596    -34.588
     907           -35.518       0.2596    995    1.9624    -36.027    -35.008
     908           -34.873      0.25518    995    1.9624    -35.373    -34.372
     909           -34.671       0.2538    995    1.9624    -35.169    -34.173
     910           -33.086      0.24305    995    1.9624    -33.563    -32.609
     911           -33.979      0.24908    995    1.9624    -34.468     -33.49
     912           -33.145      0.24344    995    1.9624    -33.622    -32.667
     913           -32.483      0.23902    995    1.9624    -32.952    -32.014
     914           -32.966      0.24224    995    1.9624    -33.441    -32.491
     915           -31.482      0.23247    995    1.9624    -31.938    -31.026
     916           -31.957      0.23556    995    1.9624    -32.419    -31.495
     917           -31.722      0.23403    995    1.9624    -32.181    -31.263
     918           -31.019      0.22949    995    1.9624    -31.469    -30.569
     919           -30.704      0.22749    995    1.9624     -31.15    -30.257
     920            -30.71      0.22753    995    1.9624    -31.156    -30.263
     921           -30.294      0.22492    995    1.9624    -30.736    -29.853
     922           -30.578       0.2267    995    1.9624    -31.023    -30.133
     923           -29.953       0.2228    995    1.9624     -30.39    -29.516
     924           -30.441      0.22584    995    1.9624    -30.884    -29.998
     925           -30.001       0.2231    995    1.9624    -30.439    -29.563
     926           -28.894      0.21639    995    1.9624    -29.319    -28.469
     927           -28.251      0.21262    995    1.9624    -28.668    -27.834
     928           -28.181      0.21222    995    1.9624    -28.598    -27.765
     929           -27.605      0.20893    995    1.9624    -28.015    -27.195
     930           -26.756      0.20422    995    1.9624    -27.157    -26.355
     931           -25.965      0.19998    995    1.9624    -26.358    -25.573
     932           -25.911       0.1997    995    1.9624    -26.303    -25.519
     933           -26.088      0.20063    995    1.9624    -26.482    -25.694
     934           -25.576      0.19795    995    1.9624    -25.964    -25.188
     935           -25.624       0.1982    995    1.9624    -26.013    -25.235
     936           -25.108      0.19555    995    1.9624    -25.491    -24.724
     937           -24.896      0.19448    995    1.9624    -25.277    -24.514
     938           -24.831      0.19416    995    1.9624    -25.212     -24.45
     939           -25.136       0.1957    995    1.9624     -25.52    -24.752
     940           -24.816      0.19409    995    1.9624    -25.197    -24.435
     941           -24.777      0.19389    995    1.9624    -25.158    -24.397
     942           -24.399      0.19202    995    1.9624    -24.776    -24.023
     943           -24.007      0.19011    995    1.9624    -24.381    -23.634
     944           -23.647      0.18839    995    1.9624    -24.016    -23.277
     945           -22.335      0.18236    995    1.9624    -22.693    -21.977
     946           -21.993      0.18085    995    1.9624    -22.348    -21.638
     947           -21.792      0.17998    995    1.9624    -22.145    -21.439
     948           -20.779      0.17569    995    1.9624    -21.124    -20.435
     949            -20.64      0.17511    995    1.9624    -20.984    -20.296
     950           -20.647      0.17514    995    1.9624    -20.991    -20.303
     951           -19.839      0.17189    995    1.9624    -20.177    -19.502
     952           -19.802      0.17174    995    1.9624    -20.139    -19.465
     953           -19.686      0.17129    995    1.9624    -20.022     -19.35
     954           -18.998      0.16864    995    1.9624    -19.329    -18.667
     955           -18.794      0.16787    995    1.9624    -19.124    -18.465
     956           -18.309      0.16607    995    1.9624    -18.635    -17.983
     957           -17.978      0.16486    995    1.9624    -18.301    -17.654
     958           -17.885      0.16453    995    1.9624    -18.208    -17.562
     959           -17.469      0.16305    995    1.9624    -17.788    -17.149
     960           -16.484      0.15967    995    1.9624    -16.797     -16.17
     961           -16.711      0.16043    995    1.9624    -17.025    -16.396
     962           -16.169      0.15862    995    1.9624     -16.48    -15.858
     963           -15.425      0.15621    995    1.9624    -15.732    -15.119
     964           -14.969      0.15478    995    1.9624    -15.273    -14.665
     965           -14.527      0.15341    995    1.9624    -14.828    -14.226
     966           -13.256      0.14966    995    1.9624    -13.549    -12.962
     967           -12.978      0.14887    995    1.9624     -13.27    -12.686
     968           -12.663      0.14799    995    1.9624    -12.953    -12.372
     969           -12.465      0.14744    995    1.9624    -12.755    -12.176
     970           -11.782      0.14559    995    1.9624    -12.067    -11.496
     971           -11.898       0.1459    995    1.9624    -12.184    -11.611
     972           -11.482       0.1448    995    1.9624    -11.766    -11.198
     973           -10.869      0.14321    995    1.9624     -11.15    -10.588
     974           -9.9923      0.14102    995    1.9624    -10.269    -9.7156
     975           -9.0426      0.13875    995    1.9624    -9.3149    -8.7704
     976           -8.2233      0.13687    995    1.9624    -8.4919    -7.9547
     977             -7.51      0.13529    995    1.9624    -7.7755    -7.2445
     978           -7.4686       0.1352    995    1.9624    -7.7339    -7.2033
     979           -7.3769      0.13501    995    1.9624    -7.6419     -7.112
     980           -7.1057      0.13442    995    1.9624    -7.3694    -6.8419
     981           -6.9835      0.13416    995    1.9624    -7.2468    -6.7202
     982           -7.3527      0.13495    995    1.9624    -7.6175    -7.0879
     983           -6.6626      0.13349    995    1.9624    -6.9246    -6.4007
     984           -6.2257      0.13259    995    1.9624    -6.4858    -5.9655
     985           -6.7355      0.13364    995    1.9624    -6.9977    -6.4732
     986           -6.2836      0.13271    995    1.9624     -6.544    -6.0232
     987           -5.6518      0.13143    995    1.9624    -5.9097    -5.3939
     988           -5.6853       0.1315    995    1.9624    -5.9434    -5.4273
     989           -5.5815      0.13129    995    1.9624    -5.8391    -5.3239
     990           -5.5543      0.13124    995    1.9624    -5.8118    -5.2967
     991           -5.0433      0.13024    995    1.9624    -5.2988    -4.7877
     992           -4.0276      0.12832    995    1.9624    -4.2794    -3.7758
     993           -4.0132      0.12829    995    1.9624     -4.265    -3.7615
     994           -3.8504        0.128    995    1.9624    -4.1016    -3.5993
     995            -3.744       0.1278    995    1.9624    -3.9948    -3.4932
     996           -3.2357      0.12689    995    1.9624    -3.4847    -2.9867
     997           -2.6995      0.12595    995    1.9624    -2.9467    -2.4524
     998           -2.4706      0.12556    995    1.9624     -2.717    -2.2242
     999           -2.2276      0.12514    995    1.9624    -2.4732     -1.982
    1000           -1.3045      0.12361    995    1.9624    -1.5471    -1.0619

Displacement unit: nanometer [nm]

Plot the stat. uncertainty of displacement

displ_std = result.Displacement_std;

figure
plot(phitrue, displ_std)
xlabel('phi');
ylabel(['Statistical uncertainty of displacement, ',result.Displacement_unit]);
title(['Statistical Uncertainty: Min: ', ...
    num2str(result.Displacement_std_min), ', Max: ', ...
    num2str(result.Displacement_std_max) ]);

Plot the displacements with expanded uncertainties

displ_fit = result.Displacement_fit;
const = result.Displacement_const;
displ_true = const*phitrue;
displ_res = displ_fit - displ_true;
ix = (result.phi_fit-phitrue) < -1;
displ_res(ix) = displ_res(ix) + 2*pi*const;

figure
plot(displ_true, displ_res ,'o')
hold
plot(displ_true, 2*displ_std ,'r-')
plot(displ_true, -2*displ_std ,'r-')
grid
xlabel('True displacement');
ylabel('Displacement Residuals');
title('Expanded Uncertainty of Fitted Displacement');
Current plot held

Plot the X residuals with the expanded uncertainties

figure
plot(phitrue,result.x_res_fit,'.')
hold
plot(phitrue,2*result.x_res_std,'r-')
plot(phitrue,-2*result.x_res_std,'r-')
grid
xlabel('True phi');
ylabel('x residuals');
title('Expanded Uncertainty of Fitted X Residuals');
Current plot held

Plot the Y residuals with the expanded uncertainties

figure
plot(phitrue,result.y_res_fit,'.')
hold
plot(phitrue,2*result.y_res_std,'r-')
plot(phitrue,-2*result.y_res_std,'r-')
grid
xlabel('True phi');
ylabel('y residuals');
title('Expanded Uncertainty of Fitted Y Residuals');
Current plot held