One of my work colleagues asked me about running a linear regression prediction system from within a Web page. So I put together a demo for him.

I had existing linear regression JavaScript code written for the node.js system, so all I had to do was refactor the input from node.js readFile to HTML FileReader, and the output from node.js console.log to an HTML textarea zone. The process was conceptually simple but was surprisingly time-consuming.

Notice that because the program runs completely on the client side, I can test the system directly in a browser using the file system instead of serving up the Web page.

For my demo, I used one of my standard synthetic datasets. The data looks like:

-0.1660,  0.4406, -0.9998, -0.3953, -0.7065,  0.4840
 0.0776, -0.1616,  0.3704, -0.5911,  0.7562,  0.1568
-0.9452,  0.3409, -0.1654,  0.1174, -0.7192,  0.8054
. . .

The first five values on each line are the predictors. The last value is the target to predict. The synthetic data was generated by a 5-10-1 neural network with random weights and biases. Therefore, the data has an underlying structure that can be predicted. There are 200 training items and 40 test items. I didn’t use the test data to save some time.

The output of my demo is:

Begin linear regression demo 

Loading data into trainX and trainY 

First three train X: 
  -0.1660   0.4406  -0.9998  -0.3953  -0.7065
   0.0776  -0.1616   0.3704  -0.5911   0.7562
  -0.9452   0.3409  -0.1654   0.1174  -0.7192

First three train y: 
   0.4840
   0.1568
   0.8054

Creating and training model 

Setting SGD lrnRate = 0.001
Setting SGD maxEpochs = 200
epoch =      0  MSE = 0.1094  acc = 0.0000
epoch =     40  MSE = 0.0027  acc = 0.5050
epoch =     80  MSE = 0.0026  acc = 0.4650
epoch =    120  MSE = 0.0026  acc = 0.4600
epoch =    160  MSE = 0.0026  acc = 0.4600
Done 

Computing model accuracy 
Train acc (within 0.15) = 0.6400
Train MSE = 0.0026

Predicting for x = 
  -0.1660   0.4406  -0.9998  -0.3953  -0.7065
Predicted y = 0.5330

End demo

The trained model scores only 64.00% accuracy on the test data (128 out of 200 correct). The model predicts poorly because linear regression assumes that the data is linear, but the demo data has a non-linear structure.

I read the source data from a local text file. There are many alternatives, such as reading from a SQL database, reading JSON data from the server, etc., etc. The first button reads the training data into memory as one big string with embedded newline characters. The second button parses the big string into an XY array-of-arrays style matrix, then extracts the predictors into a trainX array-of-arrays style matrix, and extracts the target y values into a trainY vector/array.

To keep my code small, I only read the training data and skipped the test data.

Artist Robert McGinnis (1926-2025) passed away a few weeks ago. He was tremendously prolific and popular. He produced over 1,200 paperback book covers and many famous movie posters.

McGinnis had a sort of linear style that is hard to describe but very recognizable. Here are three examples of his book covers that have an oriental theme.

Demo program. Because my annoying blog editor chokes on HTML symbols, I had to replace “{” with “{{“, “}” with “}}”, the less-than symbol with “{” and the greater-than symbol with “}”.

{!-- linearRegression.html --}
{html}
  {head}
    {script}

      var trainDataAsString = "";  // globals
      var trainX = null;
      var trainY = null;

      class LinearRegressor
      {{
        constructor(seed)
        {{
          this.seed = seed + 0.5;  // avoid 0
          this.wts;     // allocated in train()
          this.bias;    // supplied in train()
        }}

        // --------------------------------------------------

        predict(x)
        {{
          let sum = 0.0;
          for (let i = 0; i { x.length; ++i) {{
            sum += x[i] * this.wts[i];
          }}
          sum += this.bias;
          return sum;
        }}

        // --------------------------------------------------

        train(trainX, trainY, lrnRate, maxEpochs)
        {{
          let dim = trainX[0].length;    // num predictors
          this.wts = vecMake(dim, 0.0);  // allocate

          let freq = maxEpochs / 5;  // when to show progress
          let lo = -0.01; let hi = 0.01;
          for (let i = 0; i { dim; ++i) {{
            this.wts[i] = (hi - lo) * this.next() + lo;
          }}
          this.bias = (hi - lo) * this.next() + lo;

          // set up indices for shuffling
          let N = trainX.length;
          let indices = vecMake(N, 0.0);
          for (let i = 0; i { N; ++i)
            indices[i] = i;

          for (let epoch = 0; epoch { maxEpochs; ++epoch) {{
            this.shuffle(indices);
            for (let i = 0; i { N; ++i) {{
              let idx = indices[i];
              let x = trainX[idx];
              let predY = this.predict(x);
              let actualY = trainY[idx];

              // update wts
              for (let j = 0; j { dim; ++j) {{
                this.wts[j] -= 
                  lrnRate * (predY - actualY) * x[j];
              }}
              this.bias -= lrnRate * (predY - actualY);
            }} // each item

            if (epoch % freq == 0) // show progress
            {{
              let mse = this.meanSqError(trainX, trainY);
              let acc = this.accuracy(trainX, trainY, 0.10);
              let s1 = "epoch = " +
                epoch.toString().padStart(6, ' ');
              let s2 = "  MSE = " +
                mse.toFixed(4).toString();
              let s3 = "  acc = " + acc.toFixed(4).toString();
              //console.log(s1 + s2 + s3);
              //alert(s1 + s2 + s3);
              logInfo(s1 + s2 + s3);
            }}

          }} // each epoch

          // apply wt decay / L2 regularization
          // for (let j = 0; j { dim; ++j)
          //   this.wts[j] *= (1.0 - this.alpha);

        }} // train()

        // --------------------------------------------------

        accuracy(dataX, dataY, pctClose)
        {{
          let nCorrect = 0; let nWrong = 0;
          let N = dataX.length;
    
          for (let i = 0; i { N; ++i) {{
            let x = dataX[i];
            let actualY = dataY[i];
            let predY = this.predict(x);
            if (Math.abs(predY - actualY) { 
              Math.abs(pctClose * actualY)) {{
              ++nCorrect;
            }}
            else {{
              ++nWrong;
            }}
          }}
          return (nCorrect * 1.0) / (nCorrect + nWrong);
        }}

        // --------------------------------------------------

        meanSqError(dataX, dataY)
        {{
          let N = dataX.length;
          let sum = 0.0;
          for (let i = 0; i { N; ++i) {{
            let x = dataX[i];
            let actualY = dataY[i];
            let predY = this.predict(x);
            sum += (actualY - predY) * (actualY - predY);
          }}
          return sum / N;
        }}

        // --------------------------------------------------

        next()
        {{
          // return sort-of-random in [0.0, 1.0)
          let x = Math.sin(this.seed) * 1000;
          let result = x - Math.floor(x);  // [0.0,1.0)
          this.seed = result;  // for next call
          return result;
        }}

        // --------------------------------------------------

        nextInt(lo, hi)
        {{
          let x = this.next();
          return Math.trunc((hi - lo) * x + lo);
        }}

        // --------------------------------------------------

        shuffle(indices)
        {{
          // Fisher-Yates
          for (let i = 0; i { indices.length; ++i) {{
            let ri = this.nextInt(i, indices.length);
            let tmp = indices[ri];
            indices[ri] = indices[i];
            indices[i] = tmp;
            //indices[i] = i; // for testing
          }}
        }}

      }} // class LinearRegressor

      // ----------------------------------------------------

      function run()
      {{
        logInfo("\nBegin linear regression demo ");

        // 1. load data into trainX and trainY
        logInfo("\nLoading data into trainX and trainY ");
        extract();

        // 1. display training data
        logInfo("\nFirst three train X: ");
        for (let i = 0; i { 3; ++i) {{
          logInfo(vecToString(trainX[i], 4, 9));
        }}

        logInfo("\nFirst three train y: ");
        for (let i = 0; i { 3; ++i)
          logInfo(trainY[i].toFixed(4).toString().
            padStart(9, ' '));

        // 2. create and train linear regression model
        let seed = 0;
        logInfo("\nCreating and training model ");
        let model = new LinearRegressor(seed);

        let lrnRate = 0.001;
        let maxEpochs = 200;
        logInfo("\nSetting SGD lrnRate = " +
          lrnRate.toFixed(3).toString());
        logInfo("Setting SGD maxEpochs = " +
          maxEpochs.toString());
        model.train(trainX, trainY, lrnRate, maxEpochs);
        logInfo("Done ");

        // 3. evaluate
        logInfo("\nComputing model accuracy ");
        let trainAcc = model.accuracy(trainX, trainY, 0.15);
        logInfo("Train acc (within 0.15) = " +
          trainAcc.toFixed(4).toString());

        let trainMSE = model.meanSqError(trainX, trainY);
        logInfo("Train MSE = " +
          trainMSE.toFixed(4).toString());

        // 4. use model
        let x = trainX[0];
        logInfo("\nPredicting for x = ");
        logInfo(vecToString(x, 4, 9));

        let predY = model.predict(x);
        logInfo("Predicted y = " + 
          predY.toFixed(4).toString());

        logInfo("\nEnd demo");

      }} // run()

      // ----------------------------------------------------

      function logInfo(msg)
      {{
        let curr = textArea2.value;
        let update = curr + msg + "\n";
        textArea2.value = update;
      }}

      function vecToString(vec, dec, wid)
      {{
        let n = vec.length;
        let result = "";
        for (let i = 0; i { n; ++i) {{
          let x = vec[i];
          let xx = x.toFixed(dec);
          let s = xx.toString().padStart(wid, ' ');
          result += s;
        }}
        return result;
      }}

      // ----------------------------------------------------
      // file routines
      // ----------------------------------------------------

      function readTrainXYFile(input) {{
        let file = input.files[0];
        let reader = new FileReader();
        reader.readAsText(file);

        reader.onload = function() {{
          textArea1.value = reader.result;
          trainDataAsString = reader.result;
        }};

        reader.onerror = function() {{
          alert(reader.error);
        }};
      }}

      function extract()
      {{
        // extract source string into X matrix, y vector
        let comment = "#";
        let delimit = ",";
        let useCols = [0,1,2,3,4,5];  // source
        let xCols = [0,1,2,3,4];
        let yCol = 5;
        let all = trainDataAsString.trim(); // assume exists
        let lines = all.split("\n");  // array of lines

        // count number non-comment lines
        let nRows = 0;
        for (let i = 0; i { lines.length; ++i) {{
          if (!lines[i].startsWith(comment))
            ++nRows;
        }}
        let nCols = useCols.length;
        let xyDataAsMatrix = matMake(nRows, nCols, 0.0);
        let r = 0;  // ptr into lines
        let i = 0;  // ptr into result[][]
        while (r { lines.length) {{
          if (lines[r].startsWith(comment)) {{
            ++r;  // next row
          }}
          else {{
            let tokens = lines[r].split(delimit);
            for (let j = 0; j { nCols; ++j) {{
              xyDataAsMatrix[i][j] = 
                parseFloat(tokens[useCols[j]]);
            }}
            ++r;
            ++i;
          }}
        }} // while

        // 2. extract the X predictors
        // xCols = [0,1,2,3,4];
        nCols = xCols.length;
        trainX = matMake(nRows, nCols, 0.0);
        for (let i = 0; i { nRows; ++i) {{
          for (let j = 0; j { xCols.length; ++j) {{
            let jj = xCols[j];
            trainX[i][j] = xyDataAsMatrix[i][jj];
          }}
        }}
        //alert(trainX);

        // 3. extract the y targets
        // yCol = 5;
        trainY = vecMake(nRows, 0.0);
        for (let i = 0; i { nRows; ++i)
          trainY[i] = xyDataAsMatrix[i][yCol];

        //alert(trainY);
      }}

      function matMake(nRows, nCols, val)
      {{
        let result = [];
        for (let i = 0; i { nRows; ++i) {{
          result[i] = [];
          for (let j = 0; j { nCols; ++j) {{
            result[i][j] = val;
          }}
        }}
        return result;
      }} 

      function vecMake(n, val)
      {{
        let result = [];
        for (let i = 0; i { n; ++i)
          result[i] = val;
        return result;
      }}

    {/script}
  {/head}
  {body}
    {h3}Linear Regression Demo{/h3}

    {p}{input type="button" id="loadFile" 
        value="1. Select Train Data File"
        onclick="document.getElementById('file').click();"}
    {/p}
    {input type="file" style="display:none;" id="file" 
     name="file" onchange="readTrainXYFile(this)"}

    {p}{textarea id="textArea1" name="textArea1"
      cols="64" rows="8"}{/textarea}{/p}

    {p}{button onclick="run()"}
        2. Run linear regression{/button}{/p}

    {p}Messages:{/p}
    {p}{textarea id="textArea2" name="textArea2"
      cols="64" rows="38"}{/textarea}{/p}

  {/body}
{/html}  

Training data:

# synthetic_train_200.txt
#
-0.1660,  0.4406, -0.9998, -0.3953, -0.7065,  0.4840
 0.0776, -0.1616,  0.3704, -0.5911,  0.7562,  0.1568
-0.9452,  0.3409, -0.1654,  0.1174, -0.7192,  0.8054
 0.9365, -0.3732,  0.3846,  0.7528,  0.7892,  0.1345
-0.8299, -0.9219, -0.6603,  0.7563, -0.8033,  0.7955
 0.0663,  0.3838, -0.3690,  0.3730,  0.6693,  0.3206
-0.9634,  0.5003,  0.9777,  0.4963, -0.4391,  0.7377
-0.1042,  0.8172, -0.4128, -0.4244, -0.7399,  0.4801
-0.9613,  0.3577, -0.5767, -0.4689, -0.0169,  0.6861
-0.7065,  0.1786,  0.3995, -0.7953, -0.1719,  0.5569
 0.3888, -0.1716, -0.9001,  0.0718,  0.3276,  0.2500
 0.1731,  0.8068, -0.7251, -0.7214,  0.6148,  0.3297
-0.2046, -0.6693,  0.8550, -0.3045,  0.5016,  0.2129
 0.2473,  0.5019, -0.3022, -0.4601,  0.7918,  0.2613
-0.1438,  0.9297,  0.3269,  0.2434, -0.7705,  0.5171
 0.1568, -0.1837, -0.5259,  0.8068,  0.1474,  0.3307
-0.9943,  0.2343, -0.3467,  0.0541,  0.7719,  0.5581
 0.2467, -0.9684,  0.8589,  0.3818,  0.9946,  0.1092
-0.6553, -0.7257,  0.8652,  0.3936, -0.8680,  0.7018
 0.8460,  0.4230, -0.7515, -0.9602, -0.9476,  0.1996
-0.9434, -0.5076,  0.7201,  0.0777,  0.1056,  0.5664
 0.9392,  0.1221, -0.9627,  0.6013, -0.5341,  0.1533
 0.6142, -0.2243,  0.7271,  0.4942,  0.1125,  0.1661
 0.4260,  0.1194, -0.9749, -0.8561,  0.9346,  0.2230
 0.1362, -0.5934, -0.4953,  0.4877, -0.6091,  0.3810
 0.6937, -0.5203, -0.0125,  0.2399,  0.6580,  0.1460
-0.6864, -0.9628, -0.8600, -0.0273,  0.2127,  0.5387
 0.9772,  0.1595, -0.2397,  0.1019,  0.4907,  0.1611
 0.3385, -0.4702, -0.8673, -0.2598,  0.2594,  0.2270
-0.8669, -0.4794,  0.6095, -0.6131,  0.2789,  0.4700
 0.0493,  0.8496, -0.4734, -0.8681,  0.4701,  0.3516
 0.8639, -0.9721, -0.5313,  0.2336,  0.8980,  0.1412
 0.9004,  0.1133,  0.8312,  0.2831, -0.2200,  0.1782
 0.0991,  0.8524,  0.8375, -0.2102,  0.9265,  0.2150
-0.6521, -0.7473, -0.7298,  0.0113, -0.9570,  0.7422
 0.6190, -0.3105,  0.8802,  0.1640,  0.7577,  0.1056
 0.6895,  0.8108, -0.0802,  0.0927,  0.5972,  0.2214
 0.1982, -0.9689,  0.1870, -0.1326,  0.6147,  0.1310
-0.3695,  0.7858,  0.1557, -0.6320,  0.5759,  0.3773
-0.1596,  0.3581,  0.8372, -0.9992,  0.9535,  0.2071
-0.2468,  0.9476,  0.2094,  0.6577,  0.1494,  0.4132
 0.1737,  0.5000,  0.7166,  0.5102,  0.3961,  0.2611
 0.7290, -0.3546,  0.3416, -0.0983, -0.2358,  0.1332
-0.3652,  0.2438, -0.1395,  0.9476,  0.3556,  0.4170
-0.6029, -0.1466, -0.3133,  0.5953,  0.7600,  0.4334
-0.4596, -0.4953,  0.7098,  0.0554,  0.6043,  0.2775
 0.1450,  0.4663,  0.0380,  0.5418,  0.1377,  0.2931
-0.8636, -0.2442, -0.8407,  0.9656, -0.6368,  0.7429
 0.6237,  0.7499,  0.3768,  0.1390, -0.6781,  0.2185
-0.5499,  0.1850, -0.3755,  0.8326,  0.8193,  0.4399
-0.4858, -0.7782, -0.6141, -0.0008,  0.4572,  0.4197
 0.7033, -0.1683,  0.2334, -0.5327, -0.7961,  0.1776
 0.0317, -0.0457, -0.6947,  0.2436,  0.0880,  0.3345
 0.5031, -0.5559,  0.0387,  0.5706, -0.9553,  0.3107
-0.3513,  0.7458,  0.6894,  0.0769,  0.7332,  0.3170
 0.2205,  0.5992, -0.9309,  0.5405,  0.4635,  0.3532
-0.4806, -0.4859,  0.2646, -0.3094,  0.5932,  0.3202
 0.9809, -0.3995, -0.7140,  0.8026,  0.0831,  0.1600
 0.9495,  0.2732,  0.9878,  0.0921,  0.0529,  0.1289
-0.9476, -0.6792,  0.4913, -0.9392, -0.2669,  0.5966
 0.7247,  0.3854,  0.3819, -0.6227, -0.1162,  0.1550
-0.5922, -0.5045, -0.4757,  0.5003, -0.0860,  0.5863
-0.8861,  0.0170, -0.5761,  0.5972, -0.4053,  0.7301
 0.6877, -0.2380,  0.4997,  0.0223,  0.0819,  0.1404
 0.9189,  0.6079, -0.9354,  0.4188, -0.0700,  0.1907
-0.1428, -0.7820,  0.2676,  0.6059,  0.3936,  0.2790
 0.5324, -0.3151,  0.6917, -0.1425,  0.6480,  0.1071
-0.8432, -0.9633, -0.8666, -0.0828, -0.7733,  0.7784
-0.9444,  0.5097, -0.2103,  0.4939, -0.0952,  0.6787
-0.0520,  0.6063, -0.1952,  0.8094, -0.9259,  0.4836
 0.5477, -0.7487,  0.2370, -0.9793,  0.0773,  0.1241
 0.2450,  0.8116,  0.9799,  0.4222,  0.4636,  0.2355
 0.8186, -0.1983, -0.5003, -0.6531, -0.7611,  0.1511
-0.4714,  0.6382, -0.3788,  0.9648, -0.4667,  0.5950
 0.0673, -0.3711,  0.8215, -0.2669, -0.1328,  0.2677
-0.9381,  0.4338,  0.7820, -0.9454,  0.0441,  0.5518
-0.3480,  0.7190,  0.1170,  0.3805, -0.0943,  0.4724
-0.9813,  0.1535, -0.3771,  0.0345,  0.8328,  0.5438
-0.1471, -0.5052, -0.2574,  0.8637,  0.8737,  0.3042
-0.5454, -0.3712, -0.6505,  0.2142, -0.1728,  0.5783
 0.6327, -0.6297,  0.4038, -0.5193,  0.1484,  0.1153
-0.5424,  0.3282, -0.0055,  0.0380, -0.6506,  0.6613
 0.1414,  0.9935,  0.6337,  0.1887,  0.9520,  0.2540
-0.9351, -0.8128, -0.8693, -0.0965, -0.2491,  0.7353
 0.9507, -0.6640,  0.9456,  0.5349,  0.6485,  0.1059
-0.0462, -0.9737, -0.2940, -0.0159,  0.4602,  0.2606
-0.0627, -0.0852, -0.7247, -0.9782,  0.5166,  0.2977
 0.0478,  0.5098, -0.0723, -0.7504, -0.3750,  0.3335
 0.0090,  0.3477,  0.5403, -0.7393, -0.9542,  0.4415
-0.9748,  0.3449,  0.3736, -0.1015,  0.8296,  0.4358
 0.2887, -0.9895, -0.0311,  0.7186,  0.6608,  0.2057
 0.1570, -0.4518,  0.1211,  0.3435, -0.2951,  0.3244
 0.7117, -0.6099,  0.4946, -0.4208,  0.5476,  0.1096
-0.2929, -0.5726,  0.5346, -0.3827,  0.4665,  0.2465
 0.4889, -0.5572, -0.5718, -0.6021, -0.7150,  0.2163
-0.7782,  0.3491,  0.5996, -0.8389, -0.5366,  0.6516
-0.5847,  0.8347,  0.4226,  0.1078, -0.3910,  0.6134
 0.8469,  0.4121, -0.0439, -0.7476,  0.9521,  0.1571
-0.6803, -0.5948, -0.1376, -0.1916, -0.7065,  0.7156
 0.2878,  0.5086, -0.5785,  0.2019,  0.4979,  0.2980
 0.2764,  0.1943, -0.4090,  0.4632,  0.8906,  0.2960
-0.8877,  0.6705, -0.6155, -0.2098, -0.3998,  0.7107
-0.8398,  0.8093, -0.2597,  0.0614, -0.0118,  0.6502
-0.8476,  0.0158, -0.4769, -0.2859, -0.7839,  0.7715
 0.5751, -0.7868,  0.9714, -0.6457,  0.1448,  0.1175
 0.4802, -0.7001,  0.1022, -0.5668,  0.5184,  0.1090
 0.4458, -0.6469,  0.7239, -0.9604,  0.7205,  0.0779
 0.5175,  0.4339,  0.9747, -0.4438, -0.9924,  0.2879
 0.8678,  0.7158,  0.4577,  0.0334,  0.4139,  0.1678
 0.5406,  0.5012,  0.2264, -0.1963,  0.3946,  0.2088
-0.9938,  0.5498,  0.7928, -0.5214, -0.7585,  0.7687
 0.7661,  0.0863, -0.4266, -0.7233, -0.4197,  0.1466
 0.2277, -0.3517, -0.0853, -0.1118,  0.6563,  0.1767
 0.3499, -0.5570, -0.0655, -0.3705,  0.2537,  0.1632
 0.7547, -0.1046,  0.5689, -0.0861,  0.3125,  0.1257
 0.8186,  0.2110,  0.5335,  0.0094, -0.0039,  0.1391
 0.6858, -0.8644,  0.1465,  0.8855,  0.0357,  0.1845
-0.4967,  0.4015,  0.0805,  0.8977,  0.2487,  0.4663
 0.6760, -0.9841,  0.9787, -0.8446, -0.3557,  0.1509
-0.1203, -0.4885,  0.6054, -0.0443, -0.7313,  0.4854
 0.8557,  0.7919, -0.0169,  0.7134, -0.1628,  0.2002
 0.0115, -0.6209,  0.9300, -0.4116, -0.7931,  0.4052
-0.7114, -0.9718,  0.4319,  0.1290,  0.5892,  0.3661
 0.3915,  0.5557, -0.1870,  0.2955, -0.6404,  0.2954
-0.3564, -0.6548, -0.1827, -0.5172, -0.1862,  0.4622
 0.2392, -0.4959,  0.5857, -0.1341, -0.2850,  0.2470
-0.3394,  0.3947, -0.4627,  0.6166, -0.4094,  0.5325
 0.7107,  0.7768, -0.6312,  0.1707,  0.7964,  0.2757
-0.1078,  0.8437, -0.4420,  0.2177,  0.3649,  0.4028
-0.3139,  0.5595, -0.6505, -0.3161, -0.7108,  0.5546
 0.4335,  0.3986,  0.3770, -0.4932,  0.3847,  0.1810
-0.2562, -0.2894, -0.8847,  0.2633,  0.4146,  0.4036
 0.2272,  0.2966, -0.6601, -0.7011,  0.0284,  0.2778
-0.0743, -0.1421, -0.0054, -0.6770, -0.3151,  0.3597
-0.4762,  0.6891,  0.6007, -0.1467,  0.2140,  0.4266
-0.4061,  0.7193,  0.3432,  0.2669, -0.7505,  0.6147
-0.0588,  0.9731,  0.8966,  0.2902, -0.6966,  0.4955
-0.0627, -0.1439,  0.1985,  0.6999,  0.5022,  0.3077
 0.1587,  0.8494, -0.8705,  0.9827, -0.8940,  0.4263
-0.7850,  0.2473, -0.9040, -0.4308, -0.8779,  0.7199
 0.4070,  0.3369, -0.2428, -0.6236,  0.4940,  0.2215
-0.0242,  0.0513, -0.9430,  0.2885, -0.2987,  0.3947
-0.5416, -0.1322, -0.2351, -0.0604,  0.9590,  0.3683
 0.1055,  0.7783, -0.2901, -0.5090,  0.8220,  0.2984
-0.9129,  0.9015,  0.1128, -0.2473,  0.9901,  0.4776
-0.9378,  0.1424, -0.6391,  0.2619,  0.9618,  0.5368
 0.7498, -0.0963,  0.4169,  0.5549, -0.0103,  0.1614
-0.2612, -0.7156,  0.4538, -0.0460, -0.1022,  0.3717
 0.7720,  0.0552, -0.1818, -0.4622, -0.8560,  0.1685
-0.4177,  0.0070,  0.9319, -0.7812,  0.3461,  0.3052
-0.0001,  0.5542, -0.7128, -0.8336, -0.2016,  0.3803
 0.5356, -0.4194, -0.5662, -0.9666, -0.2027,  0.1776
-0.2378,  0.3187, -0.8582, -0.6948, -0.9668,  0.5474
-0.1947, -0.3579,  0.1158,  0.9869,  0.6690,  0.2992
 0.3992,  0.8365, -0.9205, -0.8593, -0.0520,  0.3154
-0.0209,  0.0793,  0.7905, -0.1067,  0.7541,  0.1864
-0.4928, -0.4524, -0.3433,  0.0951, -0.5597,  0.6261
-0.8118,  0.7404, -0.5263, -0.2280,  0.1431,  0.6349
 0.0516, -0.8480,  0.7483,  0.9023,  0.6250,  0.1959
-0.3212,  0.1093,  0.9488, -0.3766,  0.3376,  0.2735
-0.3481,  0.5490, -0.3484,  0.7797,  0.5034,  0.4379
-0.5785, -0.9170, -0.3563, -0.9258,  0.3877,  0.4121
 0.3407, -0.1391,  0.5356,  0.0720, -0.9203,  0.3458
-0.3287, -0.8954,  0.2102,  0.0241,  0.2349,  0.3247
-0.1353,  0.6954, -0.0919, -0.9692,  0.7461,  0.3338
 0.9036, -0.8982, -0.5299, -0.8733, -0.1567,  0.1187
 0.7277, -0.8368, -0.0538, -0.7489,  0.5458,  0.0830
 0.9049,  0.8878,  0.2279,  0.9470, -0.3103,  0.2194
 0.7957, -0.1308, -0.5284,  0.8817,  0.3684,  0.2172
 0.4647, -0.4931,  0.2010,  0.6292, -0.8918,  0.3371
-0.7390,  0.6849,  0.2367,  0.0626, -0.5034,  0.7039
-0.1567, -0.8711,  0.7940, -0.5932,  0.6525,  0.1710
 0.7635, -0.0265,  0.1969,  0.0545,  0.2496,  0.1445
 0.7675,  0.1354, -0.7698, -0.5460,  0.1920,  0.1728
-0.5211, -0.7372, -0.6763,  0.6897,  0.2044,  0.5217
 0.1913,  0.1980,  0.2314, -0.8816,  0.5006,  0.1998
 0.8964,  0.0694, -0.6149,  0.5059, -0.9854,  0.1825
 0.1767,  0.7104,  0.2093,  0.6452,  0.7590,  0.2832
-0.3580, -0.7541,  0.4426, -0.1193, -0.7465,  0.5657
-0.5996,  0.5766, -0.9758, -0.3933, -0.9572,  0.6800
 0.9950,  0.1641, -0.4132,  0.8579,  0.0142,  0.2003
-0.4717, -0.3894, -0.2567, -0.5111,  0.1691,  0.4266
 0.3917, -0.8561,  0.9422,  0.5061,  0.6123,  0.1212
-0.0366, -0.1087,  0.3449, -0.1025,  0.4086,  0.2475
 0.3633,  0.3943,  0.2372, -0.6980,  0.5216,  0.1925
-0.5325, -0.6466, -0.2178, -0.3589,  0.6310,  0.3568
 0.2271,  0.5200, -0.1447, -0.8011, -0.7699,  0.3128
 0.6415,  0.1993,  0.3777, -0.0178, -0.8237,  0.2181
-0.5298, -0.0768, -0.6028, -0.9490,  0.4588,  0.4356
 0.6870, -0.1431,  0.7294,  0.3141,  0.1621,  0.1632
-0.5985,  0.0591,  0.7889, -0.3900,  0.7419,  0.2945
 0.3661,  0.7984, -0.8486,  0.7572, -0.6183,  0.3449
 0.6995,  0.3342, -0.3113, -0.6972,  0.2707,  0.1712
 0.2565,  0.9126,  0.1798, -0.6043, -0.1413,  0.2893
-0.3265,  0.9839, -0.2395,  0.9854,  0.0376,  0.4770
 0.2690, -0.1722,  0.9818,  0.8599, -0.7015,  0.3954
-0.2102, -0.0768,  0.1219,  0.5607, -0.0256,  0.3949
 0.8216, -0.9555,  0.6422, -0.6231,  0.3715,  0.0801
-0.2896,  0.9484, -0.7545, -0.6249,  0.7789,  0.4370
-0.9985, -0.5448, -0.7092, -0.5931,  0.7926,  0.5402