command strategy for converting the following multi table text file into matlab array

Hello , I have the following attached file.

i need to create in the most effiecient code way.

i have a table i need to skip two first line.

then i need to read each line and and put it into a 2D array.

where i have a problem of how to read properly the line and disregard the chars which do not represent the valueble data.

after that i need to do the same thing for the next table over and over till my file ends(i dont know how many tables are there)

is there some wat i could accoplish that without making 10000 loop and read each char?

i'll be happy for some advice regarding a startegy to how properly read this file.

Thanks.

[Jon]

I'm sorry but I'm having trouble understanding what you are trying to do. I'm looking in your attached data file and I see two columns of data. When you say you "need to read each line and put it into a 2D array", I don't understand. Each line is only two values. So the "2d array" would either be 1 row by 2 columns, or 2 rows by 1 column. When you say "then i need to do the same thing for the next table", what is the next table, the next line of data? Can you provide an example of what your desired output would be?

[fima v]

Hello John, in the file i have 4 tables.

each table i need to convert into a 2D numeric variable representing [frequency , dB] structure.

Thanks.

[Jon]

You said you had 4 "data tables" but I only see three S1, S2, and S3 in the attached file. Are there really four data sets?

[fima v]

yes sorry there are 3, but it could be 20.

it will be good to have some general trick for N subtables

[Voss]

"it will be good to have some general trick for N subtables"

All approaches shown so far work for files containing any number of tables.

Answer 1

[Jon]

If you don't know how many rows there are in each data set or where the data rows begin and end then you could do this:

% read data into cell arrray
A = readcell('file.txt','commentStyle','-'); % ignore lines with ------
% find header rows
idxHdr =find(strcmp(A(:,1),'Frequency'));

% calculate starting row of each data set
startRow = idxHdr + 1;

% calculate ending row of each data set
endRow = [idxHdr(2:end)-1;size(A,1) ];


% make cell array of 2d arrays, one element for each data set
numSets = numel(idxHdr);
dataSets = cell(numSets,1); % preallocate cell array
% loop through individual data sets (each one begins with a header)
for k = 1:numSets
    dataSets{k} = cell2mat(A(startRow(k):endRow(k),1:2));
end

[Jon]

If, as in this case, you know that each data set has 1001 rows, you could just read in the data like this and save it in a 3d array (one page for each data set)

% read data into cell arrray
numSamples = 1001;
A = readcell('file.txt');
% find the numeric rows
idxNumeric = find(cellfun(@isnumeric,(A(:,1))));

% just keep the numeric values
A = A(idxNumeric,1:2);

% put them into a 3d array with a page (3rd dimension) for each dataset
data = reshape(A',2,1001,3); % reshape takes data columnwise so use transpose
data = permute(data,[2,1,3]); % undo the transpose for each 2-d data set

[Jon]

With either of these approaches you could also save the data stacked in a table with a columns for frequency and response (dB), and an additional column that gives the data set number. This allows you to use all of the power of MATLAB for dealing with grouped data in tables.

[Jon]

Ooops, for the 3d array the line A = A(idxNumeric ... should be replaced by

A = cell2mat(A(idxNumeric,1:2));

so result will be an array of doubles not a cell. So whole thing looks like:

% read data into cell arrray
numSamples = 1001;
A = readcell('file.txt');
% find the numeric rows
idxNumeric = find(cellfun(@isnumeric,(A(:,1))));

% just keep these values
A = cell2mat(A(idxNumeric,1:2));

% put them into a 3d array with a page (3rd dimension) for each dataset
data = reshape(A',2,1001,3); % reshape takes data columnwise so use transpose
data = permute(data,[2,1,3]); % undo the transpose for each 2-d data set

[Jon]

One minor improvement. I realized the find command was unecessary, you can just use logical indexing, so replace

idxNumeric = find(cellfun(@isnumeric,(A(:,1))));

with

idxNumeric = cellfun(@isnumeric,(A(:,1)));

Answer 2

[Voss]

fid = fopen('file.txt');
data = {};
while ~feof(fid)
    fgetl(fid);
    fgetl(fid);
    data{end+1} = reshape(fscanf(fid,'%f'),2,[]).';
end
fclose(fid);

disp(data) % cell array of 2D arrays

    {1001×2 double}    {1001×2 double}    {1001×2 double}

disp(data{1})

    8.0000  -16.4910
    8.0040  -16.5085
    8.0080  -16.5246
    8.0120  -16.5393
    8.0160  -16.5526
    8.0200  -16.5644
    8.0240  -16.5748
    8.0280  -16.5837
    8.0320  -16.5913
    8.0360  -16.5974
    8.0400  -16.6021
    8.0440  -16.6054
    8.0480  -16.6073
    8.0520  -16.6079
    8.0560  -16.6070
    8.0600  -16.6049
    8.0640  -16.6014
    8.0680  -16.5966
    8.0720  -16.5905
    8.0760  -16.5831
    8.0800  -16.5745
    8.0840  -16.5646
    8.0880  -16.5536
    8.0920  -16.5414
    8.0960  -16.5280
    8.1000  -16.5135
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    8.1080  -16.4812
    8.1120  -16.4634
    8.1160  -16.4446
    8.1200  -16.4249
    8.1240  -16.4042
    8.1280  -16.3825
    8.1320  -16.3600
    8.1360  -16.3365
    8.1400  -16.3123
    8.1440  -16.2872
    8.1480  -16.2613
    8.1520  -16.2346
    8.1560  -16.2073
    8.1600  -16.1792
    8.1640  -16.1504
    8.1680  -16.1210
    8.1720  -16.0910
    8.1760  -16.0604
    8.1800  -16.0293
    8.1840  -15.9976
    8.1880  -15.9654
    8.1920  -15.9327
    8.1960  -15.8996
    8.2000  -15.8661
    8.2040  -15.8321
    8.2080  -15.7978
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    8.2960  -14.9894
    8.3000  -14.9519
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    9.2200  -13.0882
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    9.2520  -13.2989
    9.2560  -13.3267
    9.2600  -13.3550
    9.2640  -13.3836
    9.2680  -13.4125
    9.2720  -13.4418
    9.2760  -13.4714
    9.2800  -13.5015
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    9.3000  -13.6570
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    9.3200  -13.8220
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    9.4000  -14.5835
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    9.6120  -17.6284
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    9.8840  -26.6141
    9.8880  -26.8565
    9.8920  -27.1054
    9.8960  -27.3612
    9.9000  -27.6243
    9.9040  -27.8949
    9.9080  -28.1734
    9.9120  -28.4603
    9.9160  -28.7558
    9.9200  -29.0605
    9.9240  -29.3746
    9.9280  -29.6988
    9.9320  -30.0333
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    9.9400  -30.7352
    9.9440  -31.1033
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    9.9520  -31.8753
    9.9560  -32.2793
    9.9600  -32.6952
    9.9640  -33.1223
    9.9680  -33.5597
    9.9720  -34.0056
    9.9760  -34.4578
    9.9800  -34.9125
    9.9840  -35.3648
    9.9880  -35.8081
    9.9920  -36.2335
    9.9960  -36.6303
   10.0000  -36.9855
   10.0040  -37.2850
   10.0080  -37.5143
   10.0120  -37.6609
   10.0160  -37.7157
   10.0200  -37.6751
   10.0240  -37.5418
   10.0280  -37.3239
   10.0320  -37.0335
   10.0360  -36.6849
   10.0400  -36.2925
   10.0440  -35.8694
   10.0480  -35.4268
   10.0520  -34.9737
   10.0560  -34.5173
   10.0600  -34.0628
   10.0640  -33.6139
   10.0680  -33.1732
   10.0720  -32.7426
   10.0760  -32.3231
   10.0800  -31.9154
   10.0840  -31.5197
   10.0880  -31.1360
   10.0920  -30.7641
   10.0960  -30.4039
   10.1000  -30.0550
   10.1040  -29.7170
   10.1080  -29.3894
   10.1120  -29.0718
   10.1160  -28.7639
   10.1200  -28.4651
   10.1240  -28.1751
   10.1280  -27.8934
   10.1320  -27.6198
   10.1360  -27.3537
   10.1400  -27.0949
   10.1440  -26.8431
   10.1480  -26.5978
   10.1520  -26.3589
   10.1560  -26.1261
   10.1600  -25.8990
   10.1640  -25.6775
   10.1680  -25.4613
   10.1720  -25.2501
   10.1760  -25.0439
   10.1800  -24.8423
   10.1840  -24.6452
   10.1880  -24.4524
   10.1920  -24.2637
   10.1960  -24.0791
   10.2000  -23.8983
   10.2040  -23.7211
   10.2080  -23.5476
   10.2120  -23.3774
   10.2160  -23.2106
   10.2200  -23.0470
   10.2240  -22.8864
   10.2280  -22.7289
   10.2320  -22.5742
   10.2360  -22.4223
   10.2400  -22.2732
   10.2440  -22.1266
   10.2480  -21.9826
   10.2520  -21.8410
   10.2560  -21.7019
   10.2600  -21.5650
   10.2640  -21.4304
   10.2680  -21.2979
   10.2720  -21.1676
   10.2760  -21.0394
   10.2800  -20.9131
   10.2840  -20.7888
   10.2880  -20.6664
   10.2920  -20.5458
   10.2960  -20.4270
   10.3000  -20.3100
   10.3040  -20.1946
   10.3080  -20.0810
   10.3120  -19.9689
   10.3160  -19.8585
   10.3200  -19.7495
   10.3240  -19.6421
   10.3280  -19.5362
   10.3320  -19.4317
   10.3360  -19.3286
   10.3400  -19.2268
   10.3440  -19.1264
   10.3480  -19.0273
   10.3520  -18.9295
   10.3560  -18.8330
   10.3600  -18.7377
   10.3640  -18.6435
   10.3680  -18.5506
   10.3720  -18.4588
   10.3760  -18.3681
   10.3800  -18.2786
   10.3840  -18.1901
   10.3880  -18.1027
   10.3920  -18.0163
   10.3960  -17.9309
   10.4000  -17.8466
   10.4040  -17.7632
   10.4080  -17.6808
   10.4120  -17.5994
   10.4160  -17.5188
   10.4200  -17.4392
   10.4240  -17.3605
   10.4280  -17.2827
   10.4320  -17.2057
   10.4360  -17.1296
   10.4400  -17.0543
   10.4440  -16.9798
   10.4480  -16.9061
   10.4520  -16.8333
   10.4560  -16.7612
   10.4600  -16.6899
   10.4640  -16.6193
   10.4680  -16.5495
   10.4720  -16.4804
   10.4760  -16.4121
   10.4800  -16.3444
   10.4840  -16.2774
   10.4880  -16.2112
   10.4920  -16.1456
   10.4960  -16.0807
   10.5000  -16.0164
   10.5040  -15.9528
   10.5080  -15.8898
   10.5120  -15.8274
   10.5160  -15.7657
   10.5200  -15.7046
   10.5240  -15.6441
   10.5280  -15.5842
   10.5320  -15.5248
   10.5360  -15.4661
   10.5400  -15.4079
   10.5440  -15.3502
   10.5480  -15.2932
   10.5520  -15.2367
   10.5560  -15.1807
   10.5600  -15.1252
   10.5640  -15.0703
   10.5680  -15.0159
   10.5720  -14.9620
   10.5760  -14.9086
   10.5800  -14.8558
   10.5840  -14.8034
   10.5880  -14.7515
   10.5920  -14.7001
   10.5960  -14.6491
   10.6000  -14.5987
   10.6040  -14.5487
   10.6080  -14.4991
   10.6120  -14.4500
   10.6160  -14.4014
   10.6200  -14.3532
   10.6240  -14.3055
   10.6280  -14.2581
   10.6320  -14.2113
   10.6360  -14.1648
   10.6400  -14.1187
   10.6440  -14.0731
   10.6480  -14.0279
   10.6520  -13.9831
   10.6560  -13.9387
   10.6600  -13.8947
   10.6640  -13.8511
   10.6680  -13.8078
   10.6720  -13.7650
   10.6760  -13.7225
   10.6800  -13.6805
   10.6840  -13.6387
   10.6880  -13.5974
   10.6920  -13.5564
   10.6960  -13.5158
   10.7000  -13.4756
   10.7040  -13.4357
   10.7080  -13.3962
   10.7120  -13.3570
   10.7160  -13.3181
   10.7200  -13.2796
   10.7240  -13.2414
   10.7280  -13.2036
   10.7320  -13.1661
   10.7360  -13.1290
   10.7400  -13.0921
   10.7440  -13.0556
   10.7480  -13.0194
   10.7520  -12.9835
   10.7560  -12.9480
   10.7600  -12.9127
   10.7640  -12.8778
   10.7680  -12.8431
   10.7720  -12.8088
   10.7760  -12.7748
   10.7800  -12.7411
   10.7840  -12.7076
   10.7880  -12.6745
   10.7920  -12.6416
   10.7960  -12.6091
   10.8000  -12.5768
   10.8040  -12.5448
   10.8080  -12.5131
   10.8120  -12.4817
   10.8160  -12.4506
   10.8200  -12.4197
   10.8240  -12.3891
   10.8280  -12.3588
   10.8320  -12.3287
   10.8360  -12.2989
   10.8400  -12.2694
   10.8440  -12.2401
   10.8480  -12.2111
   10.8520  -12.1824
   10.8560  -12.1539
   10.8600  -12.1257
   10.8640  -12.0977
   10.8680  -12.0699
   10.8720  -12.0425
   10.8760  -12.0152
   10.8800  -11.9882
   10.8840  -11.9615
   10.8880  -11.9350
   10.8920  -11.9087
   10.8960  -11.8827
   10.9000  -11.8569
   10.9040  -11.8314
   10.9080  -11.8061
   10.9120  -11.7810
   10.9160  -11.7562
   10.9200  -11.7315
   10.9240  -11.7071
   10.9280  -11.6830
   10.9320  -11.6590
   10.9360  -11.6353
   10.9400  -11.6118
   10.9440  -11.5885
   10.9480  -11.5655
   10.9520  -11.5427
   10.9560  -11.5200
   10.9600  -11.4976
   10.9640  -11.4754
   10.9680  -11.4535
   10.9720  -11.4317
   10.9760  -11.4101
   10.9800  -11.3888
   10.9840  -11.3676
   10.9880  -11.3467
   10.9920  -11.3260
   10.9960  -11.3054
   11.0000  -11.2851
   11.0040  -11.2650
   11.0080  -11.2451
   11.0120  -11.2254
   11.0160  -11.2058
   11.0200  -11.1865
   11.0240  -11.1674
   11.0280  -11.1485
   11.0320  -11.1297
   11.0360  -11.1112
   11.0400  -11.0928
   11.0440  -11.0747
   11.0480  -11.0567
   11.0520  -11.0389
   11.0560  -11.0213
   11.0600  -11.0039
   11.0640  -10.9867
   11.0680  -10.9697
   11.0720  -10.9528
   11.0760  -10.9361
   11.0800  -10.9197
   11.0840  -10.9034
   11.0880  -10.8873
   11.0920  -10.8713
   11.0960  -10.8556
   11.1000  -10.8400
   11.1040  -10.8246
   11.1080  -10.8094
   11.1120  -10.7944
   11.1160  -10.7795
   11.1200  -10.7648
   11.1240  -10.7503
   11.1280  -10.7360
   11.1320  -10.7218
   11.1360  -10.7078
   11.1400  -10.6940
   11.1440  -10.6804
   11.1480  -10.6669
   11.1520  -10.6536
   11.1560  -10.6405
   11.1600  -10.6275
   11.1640  -10.6147
   11.1680  -10.6021
   11.1720  -10.5897
   11.1760  -10.5774
   11.1800  -10.5653
   11.1840  -10.5533
   11.1880  -10.5416
   11.1920  -10.5300
   11.1960  -10.5185
   11.2000  -10.5072
   11.2040  -10.4961
   11.2080  -10.4852
   11.2120  -10.4744
   11.2160  -10.4638
   11.2200  -10.4533
   11.2240  -10.4431
   11.2280  -10.4329
   11.2320  -10.4230
   11.2360  -10.4132
   11.2400  -10.4035
   11.2440  -10.3941
   11.2480  -10.3848
   11.2520  -10.3756
   11.2560  -10.3667
   11.2600  -10.3578
   11.2640  -10.3492
   11.2680  -10.3407
   11.2720  -10.3324
   11.2760  -10.3242
   11.2800  -10.3162
   11.2840  -10.3083
   11.2880  -10.3007
   11.2920  -10.2931
   11.2960  -10.2858
   11.3000  -10.2786
   11.3040  -10.2716
   11.3080  -10.2647
   11.3120  -10.2580
   11.3160  -10.2514
   11.3200  -10.2451
   11.3240  -10.2388
   11.3280  -10.2328
   11.3320  -10.2269
   11.3360  -10.2212
   11.3400  -10.2156
   11.3440  -10.2102
   11.3480  -10.2050
   11.3520  -10.1999
   11.3560  -10.1950
   11.3600  -10.1903
   11.3640  -10.1857
   11.3680  -10.1813
   11.3720  -10.1770
   11.3760  -10.1730
   11.3800  -10.1691
   11.3840  -10.1653
   11.3880  -10.1617
   11.3920  -10.1583
   11.3960  -10.1551
   11.4000  -10.1521
   11.4040  -10.1492
   11.4080  -10.1464
   11.4120  -10.1439
   11.4160  -10.1415
   11.4200  -10.1393
   11.4240  -10.1373
   11.4280  -10.1354
   11.4320  -10.1337
   11.4360  -10.1322
   11.4400  -10.1309
   11.4440  -10.1298
   11.4480  -10.1288
   11.4520  -10.1280
   11.4560  -10.1274
   11.4600  -10.1270
   11.4640  -10.1267
   11.4680  -10.1266
   11.4720  -10.1268
   11.4760  -10.1271
   11.4800  -10.1276
   11.4840  -10.1282
   11.4880  -10.1291
   11.4920  -10.1302
   11.4960  -10.1314
   11.5000  -10.1328
   11.5040  -10.1345
   11.5080  -10.1363
   11.5120  -10.1383
   11.5160  -10.1405
   11.5200  -10.1429
   11.5240  -10.1456
   11.5280  -10.1484
   11.5320  -10.1514
   11.5360  -10.1546
   11.5400  -10.1581
   11.5440  -10.1617
   11.5480  -10.1655
   11.5520  -10.1696
   11.5560  -10.1739
   11.5600  -10.1783
   11.5640  -10.1830
   11.5680  -10.1880
   11.5720  -10.1931
   11.5760  -10.1985
   11.5800  -10.2040
   11.5840  -10.2098
   11.5880  -10.2159
   11.5920  -10.2221
   11.5960  -10.2286
   11.6000  -10.2353
   11.6040  -10.2423
   11.6080  -10.2495
   11.6120  -10.2569
   11.6160  -10.2646
   11.6200  -10.2725
   11.6240  -10.2807
   11.6280  -10.2891
   11.6320  -10.2978
   11.6360  -10.3067
   11.6400  -10.3159
   11.6440  -10.3254
   11.6480  -10.3351
   11.6520  -10.3450
   11.6560  -10.3553
   11.6600  -10.3658
   11.6640  -10.3766
   11.6680  -10.3876
   11.6720  -10.3990
   11.6760  -10.4106
   11.6800  -10.4225
   11.6840  -10.4347
   11.6880  -10.4472
   11.6920  -10.4599
   11.6960  -10.4730
   11.7000  -10.4864
   11.7040  -10.5001
   11.7080  -10.5141
   11.7120  -10.5284
   11.7160  -10.5430
   11.7200  -10.5580
   11.7240  -10.5732
   11.7280  -10.5888
   11.7320  -10.6048
   11.7360  -10.6210
   11.7400  -10.6376
   11.7440  -10.6546
   11.7480  -10.6719
   11.7520  -10.6896
   11.7560  -10.7076
   11.7600  -10.7259
   11.7640  -10.7447
   11.7680  -10.7638
   11.7720  -10.7833
   11.7760  -10.8032
   11.7800  -10.8234
   11.7840  -10.8441
   11.7880  -10.8651
   11.7920  -10.8866
   11.7960  -10.9084
   11.8000  -10.9307
   11.8040  -10.9534
   11.8080  -10.9765
   11.8120  -11.0001
   11.8160  -11.0241
   11.8200  -11.0485
   11.8240  -11.0734
   11.8280  -11.0987
   11.8320  -11.1245
   11.8360  -11.1508
   11.8400  -11.1775
   11.8440  -11.2048
   11.8480  -11.2325
   11.8520  -11.2607
   11.8560  -11.2894
   11.8600  -11.3187
   11.8640  -11.3484
   11.8680  -11.3787
   11.8720  -11.4096
   11.8760  -11.4409
   11.8800  -11.4729
   11.8840  -11.5053
   11.8880  -11.5384
   11.8920  -11.5720
   11.8960  -11.6063
   11.9000  -11.6411
   11.9040  -11.6765
   11.9080  -11.7126
   11.9120  -11.7493
   11.9160  -11.7866
   11.9200  -11.8246
   11.9240  -11.8632
   11.9280  -11.9025
   11.9320  -11.9425
   11.9360  -11.9832
   11.9400  -12.0246
   11.9440  -12.0667
   11.9480  -12.1095
   11.9520  -12.1531
   11.9560  -12.1974
   11.9600  -12.2425
   11.9640  -12.2884
   11.9680  -12.3351
   11.9720  -12.3826
   11.9760  -12.4310
   11.9800  -12.4802
   11.9840  -12.5302
   11.9880  -12.5811
   11.9920  -12.6329
   11.9960  -12.6856
   12.0000  -12.7392

If you know beforehand that all tables in the file are the same size, then it may be convenient to use a 3D array instead of a cell array of 2D matrices.

[fima v]

Hello VOS, could you please explain the logc of this line?

what is "end+1"?(end is the ending line of the loop its not a variable)

the reshape command is also intresting,your read the file into floating values but what is the meaning of 2,[] ?

data{end+1} = reshape(fscanf(fid,'%f'),2,[]).';

Thanks.

[Voss]

data is initially an empty cell array:

data = {};

Then, inside the loop, each time a table is read from the file, it goes into a new cell in data. That's what data{end+1} = ... does

data{end+1} = stuff; % add a new cell to the end of data, containing 'stuff'

From the documentation: "end also represents the last index of an array. For example, X(end) is the last element of X, and X(3:end) selects the third through final elements of X." (Reference: end)

reshape is there because the elements of each table are read in the order they are in the file, i.e., (row 1, col 1) then (row 1, col 2) then (row 2, col 1) and so on. So, reshaping to two rows then transposing gives you a two-column matrix with the elements in the right order as in the file.

fid = fopen('file.txt');
data = {};
while ~feof(fid)
    fgetl(fid);
    fgetl(fid);
    temp = fscanf(fid,'%f') % notice the order of the elements shown below
    data{end+1} = reshape(temp,2,[]).';
end

temp = 2002×1

8.0000 -16.4910 8.0040 -16.5085 8.0080 -16.5246 8.0120 -16.5393 8.0160 -16.5526

temp = 2002×1

8.0000 -3.1159 8.0040 -3.1165 8.0080 -3.1172 8.0120 -3.1178 8.0160 -3.1185

temp = 2002×1

8.0000 -3.1159 8.0040 -3.1165 8.0080 -3.1172 8.0120 -3.1178 8.0160 -3.1185

fclose(fid);

disp(data) % cell array of 2D arrays

    {1001×2 double}    {1001×2 double}    {1001×2 double}

disp(data{1})

    8.0000  -16.4910
    8.0040  -16.5085
    8.0080  -16.5246
    8.0120  -16.5393
    8.0160  -16.5526
    8.0200  -16.5644
    8.0240  -16.5748
    8.0280  -16.5837
    8.0320  -16.5913
    8.0360  -16.5974
    8.0400  -16.6021
    8.0440  -16.6054
    8.0480  -16.6073
    8.0520  -16.6079
    8.0560  -16.6070
    8.0600  -16.6049
    8.0640  -16.6014
    8.0680  -16.5966
    8.0720  -16.5905
    8.0760  -16.5831
    8.0800  -16.5745
    8.0840  -16.5646
    8.0880  -16.5536
    8.0920  -16.5414
    8.0960  -16.5280
    8.1000  -16.5135
    8.1040  -16.4978
    8.1080  -16.4812
    8.1120  -16.4634
    8.1160  -16.4446
    8.1200  -16.4249
    8.1240  -16.4042
    8.1280  -16.3825
    8.1320  -16.3600
    8.1360  -16.3365
    8.1400  -16.3123
    8.1440  -16.2872
    8.1480  -16.2613
    8.1520  -16.2346
    8.1560  -16.2073
    8.1600  -16.1792
    8.1640  -16.1504
    8.1680  -16.1210
    8.1720  -16.0910
    8.1760  -16.0604
    8.1800  -16.0293
    8.1840  -15.9976
    8.1880  -15.9654
    8.1920  -15.9327
    8.1960  -15.8996
    8.2000  -15.8661
    8.2040  -15.8321
    8.2080  -15.7978
    8.2120  -15.7631
    8.2160  -15.7281
    8.2200  -15.6928
    8.2240  -15.6571
    8.2280  -15.6213
    8.2320  -15.5851
    8.2360  -15.5488
    8.2400  -15.5123
    8.2440  -15.4755
    8.2480  -15.4386
    8.2520  -15.4016
    8.2560  -15.3644
    8.2600  -15.3272
    8.2640  -15.2898
    8.2680  -15.2524
    8.2720  -15.2149
    8.2760  -15.1773
    8.2800  -15.1398
    8.2840  -15.1022
    8.2880  -15.0646
    8.2920  -15.0270
    8.2960  -14.9894
    8.3000  -14.9519
    8.3040  -14.9145
    8.3080  -14.8770
    8.3120  -14.8397
    8.3160  -14.8025
    8.3200  -14.7653
    8.3240  -14.7282
    8.3280  -14.6913
    8.3320  -14.6545
    8.3360  -14.6178
    8.3400  -14.5812
    8.3440  -14.5448
    8.3480  -14.5086
    8.3520  -14.4725
    8.3560  -14.4365
    8.3600  -14.4008
    8.3640  -14.3652
    8.3680  -14.3299
    8.3720  -14.2947
    8.3760  -14.2597
    8.3800  -14.2249
    8.3840  -14.1904
    8.3880  -14.1560
    8.3920  -14.1219
    8.3960  -14.0880
    8.4000  -14.0544
    8.4040  -14.0209
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