I like to write code every day. Writing code is a skill that must be practiced, and I enjoy writing code. Over the course of my career, I saw countless colleagues move from an engineering role to an engineering-management role, and they all lost their coding ability with surprising speed.
I decided to combine quadratic regression (QR) with nearest neighbors (NN) regression. The idea is simple: create a container class that holds a QR model, and a NN model. After the two component models are trained independently, the hybrid model prediction is just a weights average of the QR prediction and the NN prediction.
The output of a demo, with basic QR, and basic NN with number nearest neighbors = 3, and the QR model prediction weight = 0.80 and the NN prediction weight = 0.20:
Begin C# hybrid quadratic regression + nearest neighbors regression Loading synthetic train (200) and test (40) data Done 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 Create hybrid quadratic regression + nearest neighbors model Setting seed for QR model = 0 Setting nNeighbors for NN model = 3 Setting QR predict weight = 0.80 Setting NN predict weight = 0.20 Done Training hybrid model Done QR model base weights: -0.2630 0.0354 -0.0421 0.0341 -0.1124 Evaluating hybrid model Accuracy train (within 0.10) = 0.9050 Accuracy test (within 0.10) = 0.9250 MSE train = 0.0003 MSE test = 0.0004 Predicting for x = -0.1660 0.4406 -0.9998 -0.3953 -0.7065 Predicted y = 0.4931 End demo
Of course, the choice of combining QR and NN is arbitrary. Any regression techniques can be used (for example, linear regression, kernel ridge regression, support vector regression, neural network regression, random forest regression, gradient boost regression). And you can use more than two regression techniques.
In practice, I like to use regression techniques that are different from each other (because they will predict different data patterns differently), and techniques with fewer architecture and training parameters (to avoid combinatorial explosion).
The Predict() and Train() methods are simple, because all of the work is done by the component models:
public class Hybid_QR_NN
{
. . .
public double Predict(double[] x)
{
double predQR = this.qrModel.Predict(x);
double predNN = this.nnModel.Predict(x);
double result =
(predQR * this.weights[0]) +
(predNN * this.weights[1]);
return result;
}
// ------------------------------------------------------
public void Train(double[][] trainX, double[] trainY)
{
this.qrModel.Train(trainX, trainY);
this.nnModel.Train(trainX, trainY);
}
. . .
public class QuadraticRegressor { . . . }
public class QRHouseholder { . . . } // helper for QR
public class NearestNeighborsRegressor { . . . }
Instead of wrapping the hybrid regressor in a container class, Hybid_QR_NN_Regressor, it’s perfectly possible to just use the QuadraticRegressor class and the NearestNeighborsRegressor class separately, and then compute a weighted average of their Predict() methods. But putting everything into a container class keeps things more organized and easier to work with.
The scikit-learn library provides a VotingRegressor module that combines two or more scikit regression models.
Most of my friends, and me, get obsessed with all kinds of strange things. For reasons that are unknown to me, I am moderately obsessed with movies that feature a creature that makes noises that are translated to “chittering” in the closed caption text. The are an amazing number of chittering instances in science fiction movies, but you’ll only notice these chitterings if you’re looking for them.
Left: In the science fiction movie “War Machine” (2026), a group of soldiers on a training mission in a remote forested area encounter an alien invasion led by a seemingly invincible robot killing machine. The war machine doesn’t chitter, but as the soldiers elude the machine at night, I got a nice chittering. Not a bad movie. I give it a B grade. Nothing special — just good old-fashioned action.
Right: In the science fiction movie “The Tomorrow War” (2021), in the year 2051, aliens invade Earth with fearsome bio-weapons. Humanity is on the verge of extinction, but is able to use a time-travel device to import humans from the present time of 2021. A clever idea. I liked this movie quite a bit more than my friends. I give it a B grade. Most of my friends grade it out at a C or even C-.
Demo program. Replace “lt” (less than), “gt”, “lte”, “gte” with Boolean operator symbols (my blog editor chokes on symbols).
using System;
using System.IO;
using System.Collections.Generic;
namespace Hybrid_QR_NN_Regression
{
internal class HybridProgram
{
static void Main(string[] args)
{
Console.WriteLine("\nBegin C# hybrid quadratic " +
"regression + nearest neighbors regression ");
// 1. load data
Console.WriteLine("\nLoading synthetic train" +
" (200) and test (40) data");
string trainFile =
"..\\..\\..\\Data\\synthetic_train_200.txt";
int[] colsX = new int[] { 0, 1, 2, 3, 4 };
int colY = 5;
double[][] trainX =
MatLoad(trainFile, colsX, ',', "#");
double[] trainY =
MatToVec(MatLoad(trainFile,
new int[] { colY }, ',', "#"));
string testFile =
"..\\..\\..\\Data\\synthetic_test_40.txt";
double[][] testX =
MatLoad(testFile, colsX, ',', "#");
double[] testY =
MatToVec(MatLoad(testFile,
new int[] { colY }, ',', "#"));
Console.WriteLine("Done ");
Console.WriteLine("\nFirst three train X: ");
for (int i = 0; i "lt" 3; ++i)
VecShow(trainX[i], 4, 8);
Console.WriteLine("\nFirst three train y: ");
for (int i = 0; i "lt" 3; ++i)
Console.WriteLine(trainY[i].ToString("F4").
PadLeft(8));
// 2. create and train model
Console.WriteLine("\nCreating hybrid quadratic " +
"regression + nearest neighbors model ");
int nNeighbors = 3;
int seed = 0;
double[] weights = new double[] { 0.80, 0.20 };
Console.WriteLine("Setting seed for QR model = " +
seed);
Console.WriteLine("Setting nNeighbors for NN model = " +
nNeighbors);
Console.WriteLine("Setting QR predict weight = " +
weights[0].ToString("F2"));
Console.WriteLine("Setting NN predict weight = " +
weights[1].ToString("F2"));
Hybid_QR_NN model =
new Hybid_QR_NN(nNeighbors, seed, weights);
Console.WriteLine("Done ");
Console.WriteLine("\nTraining hybrid model ");
model.Train(trainX, trainY); // train component models
Console.WriteLine("Done ");
// 3. show model weights
Console.WriteLine("\nQR model base weights: ");
int dim = trainX[0].Length;
for (int i = 0; i "lt" dim; ++i)
Console.Write(model.qrModel.weights[i].
ToString("F4").PadLeft(8));
Console.WriteLine("");
// Console.WriteLine("\nModel quadratic weights: ");
// Console.WriteLine("\nModel interaction weights: ");
// 4. evaluate model
Console.WriteLine("\nEvaluating hybrid model ");
double accTrain = model.Accuracy(trainX, trainY, 0.10);
Console.WriteLine("Accuracy train (within 0.10) = " +
accTrain.ToString("F4"));
double accTest = model.Accuracy(testX, testY, 0.10);
Console.WriteLine("Accuracy test (within 0.10) = " +
accTest.ToString("F4"));
double mseTrain = model.MSE(trainX, trainY);
Console.WriteLine("\nMSE train = " +
mseTrain.ToString("F4"));
double mseTest = model.MSE(testX, testY);
Console.WriteLine("MSE test = " +
mseTest.ToString("F4"));
// 5. use model
double[] x = trainX[0];
Console.WriteLine("\nPredicting for x = ");
VecShow(x, 4, 9);
double predY = model.Predict(x);
Console.WriteLine("\nPredicted y = " +
predY.ToString("F4"));
// 6. TODO: implement model Save() and Load()
Console.WriteLine("\nEnd demo ");
Console.ReadLine();
} // Main
// ------------------------------------------------------
// helpers for Main(): MatLoad(), MatToVec(), VecShow()
// ------------------------------------------------------
static double[][] MatLoad(string fn, int[] usecols,
char sep, string comment)
{
List"lt"double[]"gt" result =
new List"lt"double[]"gt"();
string line = "";
FileStream ifs = new FileStream(fn, FileMode.Open);
StreamReader sr = new StreamReader(ifs);
while ((line = sr.ReadLine()) != null)
{
if (line.StartsWith(comment) == true)
continue;
string[] tokens = line.Split(sep);
List"lt"double"gt" lst = new List"lt"double"gt"();
for (int j = 0; j "lt" usecols.Length; ++j)
lst.Add(double.Parse(tokens[usecols[j]]));
double[] row = lst.ToArray();
result.Add(row);
}
sr.Close(); ifs.Close();
return result.ToArray();
}
static double[] MatToVec(double[][] M)
{
int nRows = M.Length;
int nCols = M[0].Length;
double[] result = new double[nRows * nCols];
int k = 0;
for (int i = 0; i "lt" nRows; ++i)
for (int j = 0; j "lt" nCols; ++j)
result[k++] = M[i][j];
return result;
}
static void VecShow(double[] vec, int dec, int wid)
{
for (int i = 0; i "lt" vec.Length; ++i)
Console.Write(vec[i].ToString("F" + dec).
PadLeft(wid));
Console.WriteLine("");
}
} // class Program
// ========================================================
public class Hybid_QR_NN_Regressor
{
// training parameters for QR and kNN
// QR: no parameters needed
// kNN: only nNeighbors needed
public int nNeighbors;
private Random rnd; // not used w/ Pinv training
public double[] weights = new double[0]; // each model
public QuadraticRegressor qrModel;
public NearestNeighborsRegressor nnModel;
// ------------------------------------------------------
public Hybid_QR_NN_Regressor(int nNeighbors, int seed,
double[] weights)
{
this.nNeighbors = nNeighbors;
this.rnd = new Random(seed);
this.weights = weights;
this.qrModel =
new QuadraticRegressor(seed);
this.nnModel =
new NearestNeighborsRegressor(nNeighbors);
}
// ------------------------------------------------------
public double Predict(double[] x)
{
double predQR = this.qrModel.Predict(x);
double predNN = this.nnModel.Predict(x);
double result =
(predQR * this.weights[0]) + (predNN * this.weights[1]);
return result;
}
// ------------------------------------------------------
public void Train(double[][] trainX, double[] trainY)
{
this.qrModel.Train(trainX, trainY);
this.nnModel.Train(trainX, trainY);
}
// ------------------------------------------------------
public double MSE(double[][] dataX,
double[] dataY)
{
int n = dataX.Length;
double sum = 0.0;
for (int i = 0; i "lt" n; ++i)
{
double actualY = dataY[i];
double predY = this.Predict(dataX[i]);
sum += (actualY - predY) * (actualY - predY);
}
return sum / n;
}
// ------------------------------------------------------
public double Accuracy(double[][] dataX, double[] dataY,
double pctClose)
{
int numCorrect = 0; int numWrong = 0;
for (int i = 0; i "lt" dataX.Length; ++i)
{
double actualY = dataY[i];
double predY = this.Predict(dataX[i]);
if (Math.Abs(predY - actualY) "lt"
Math.Abs(pctClose * actualY))
++numCorrect;
else
++numWrong;
}
return (numCorrect * 1.0) / (numWrong + numCorrect);
}
// ------------------------------------------------------
} // class Hybid_QR_NN
// ========================================================
public class QuadraticRegressor
{
public double[] weights; // regular, quad, interactions
public double bias;
private Random rnd; // not used w/ Pinv training
public QuadraticRegressor(int seed = 0)
{
this.weights = new double[0]; // empty, but not null
this.bias = 0; // dummy value
this.rnd = new Random(seed);
}
// ------------------------------------------------------
public double Predict(double[] x)
{
int dim = x.Length;
double result = 0.0;
int p = 0; // points into this.weights
for (int i = 0; i "lt" dim; ++i) // base terms
result += x[i] * this.weights[p++];
for (int i = 0; i "lt" dim; ++i) // quadratic terms
result += (x[i] * x[i]) * this.weights[p++];
for (int i = 0; i "lt" dim-1; ++i) // interactions
for (int j = i+1; j "lt" dim; ++j)
result += (x[i] * x[j]) * this.weights[p++];
result += this.bias;
return result;
}
// ------------------------------------------------------
public void Train(double[][] trainX, double[] trainY)
{
// train using MP pseudo-inverse QR-Householder
// no regulaization
// w = pinv(designX) * y
int nRows = trainX.Length; // not used
int dim = trainX[0].Length;
int nInteractions = (dim * (dim - 1)) / 2;
this.weights = new double[dim + dim + nInteractions];
double[][] Xa = MatAugment(trainX); // add quad cols
double[][] X = MatToDesign(Xa); // add 1.0s col
double[][] Xpinv = QRHouseholder.MatPinv(X);
double[] biasAndWts = MatVecProd(Xpinv, trainY);
this.bias = biasAndWts[0]; // bias is at [0]
for (int i = 1; i "lt" biasAndWts.Length; ++i)
this.weights[i - 1] = biasAndWts[i];
return;
}
// ------------------------------------------------------
// ------------------------------------------------------
private static double[][] MatAugment(double[][] trainX)
{
// add quadratic and interaction columns
int nRows = trainX.Length; // src and dest
int dim = trainX[0].Length; // src
int nInteractions = dim * (dim - 1) / 2;
int nColsDest = dim + dim + nInteractions;
double[][] result = new double[nRows][];
for (int i = 0; i "lt" nRows; i++)
result[i] = new double[nColsDest];
for (int i = 0; i "lt" nRows; ++i)
{
int p = 0; // points to column of result
for (int j = 0; j "lt" dim; ++j) // base
result[i][p++] = trainX[i][j];
for (int j = 0; j "lt" dim; ++j) // quadratic
result[i][p++] = trainX[i][j] * trainX[i][j];
for (int j = 0; j "lt" nInteractions-1; ++j)
for (int k = j+1; k "lt" dim; ++k)
result[i][p++] = trainX[i][j] * trainX[i][k];
}
return result;
}
// ------------------------------------------------------
private static double[][] MatToDesign(double[][] X)
{
// add leading column of 1.0s to handle bias term
int nRows = X.Length; // src and dest
int dim = X[0].Length;
double[][] result = new double[nRows][];
for (int i = 0; i "lt" nRows; ++i)
result[i] = new double[dim + 1]; // extra col
for (int i = 0; i "lt" nRows; ++i)
{
result[i][0] = 1.0;
for (int j = 1; j "lt" result[0].Length; ++j)
{
result[i][j] = X[i][j - 1];
}
}
return result;
}
// ------------------------------------------------------
private static double[] MatVecProd(double[][] M,
double[] v)
{
// helper for Train()
int nRows = M.Length;
int nCols = M[0].Length;
int n = v.Length;
if (nCols != n)
throw new Exception("non-comform in MatVecProd");
double[] result = new double[nRows];
for (int i = 0; i "lt" nRows; ++i)
for (int k = 0; k "lt" nCols; ++k)
result[i] += M[i][k] * v[k];
return result;
}
// ------------------------------------------------------
} // class QuadraticRegressor
// ========================================================
public class QRHouseholder
{
// for class QuadraticRegressor Train()
// container for MP pseudo-inverse via QR-Householder
// A = Q * R
// pinv(A) = inv(R) * inv(Q) note order matters
// = inv upper tri (easy) * transpose (easy)
public static double[][] MatPinv(double[][] M)
{
double[][] Q; double[][] R;
MatDecompQR(M, out Q, out R); // Householder
double[][] Ri = MatInvUpperTri(R);
double[][] Qi = MatTranspose(Q);
double[][] result = MatProduct(Ri, Qi);
return result;
}
// ------------------------------------------------------
public static double[][] MatInvUpperTri(double[][] U)
{
int n = U.Length; // must be square matrix
double[][] result = MatMake(n, n);
for (int i = 0; i "lt" n; ++i)
result[i][i] = 1.0;
for (int k = 0; k "lt" n; ++k)
{
for (int j = 0; j "lt" n; ++j)
{
for (int i = 0; i "lt" k; ++i)
{
result[j][k] -= result[j][i] * U[i][k];
}
result[j][k] /= U[k][k];
}
}
return result;
}
// ------------------------------------------------------
public static double[][] MatMake(int nRows, int nCols)
{
double[][] result = new double[nRows][];
for (int i = 0; i "lt" nRows; ++i)
result[i] = new double[nCols];
return result;
}
// ------------------------------------------------------
public static double[][] MatTranspose(double[][] M)
{
int nRows = M.Length;
int nCols = M[0].Length;
double[][] result = MatMake(nCols, nRows);
for (int i = 0; i "lt" nRows; ++i)
for (int j = 0; j "lt" nCols; ++j)
result[j][i] = M[i][j];
return result;
}
// ------------------------------------------------------
public static double[][] MatProduct(double[][] A,
double[][] B)
{
int aRows = A.Length; int aCols = A[0].Length;
int bRows = B.Length; int bCols = B[0].Length;
if (aCols != bRows)
throw new Exception("Non-conformable matrices");
double[][] result = new double[aRows][];
for (int i = 0; i "lt" aRows; ++i)
result[i] = new double[bCols];
for (int i = 0; i "lt" aRows; ++i) // each row of A
for (int j = 0; j "lt" bCols; ++j) // each col of B
for (int k = 0; k "lt" aCols; ++k)
result[i][j] += A[i][k] * B[k][j];
return result;
}
// ------------------------------------------------------
public static void MatDecompQR(double[][] A,
out double[][] Q, out double[][] R)
{
// Householder algorithm
int m = A.Length; int n = A[0].Length;
if (m "lt" n)
Console.WriteLine("FATAL: nRows must be gte nCols");
double[][] QQ = MatMake(m, m); // working full Q
for (int i = 0; i "lt" m; ++i)
QQ[i][i] = 1.0; // identity matrix
double[][] RR = MatMake(m, n);
for (int i = 0; i "lt" m; ++i)
for (int j = 0; j "lt" n; ++j)
RR[i][j] = A[i][j]; // copy of A is working R
int k = Math.Min(m, n); // or just use n
for (int j = 0; j "lt" k; ++j) // main processing loop
{
int xn = m - j;
double[] x = new double[xn];
for (int i = 0; i "lt" xn; ++i)
x[i] = RR[j + i][j];
double ss = 0.0;
for (int i = 0; i "lt" xn; ++i)
ss += x[i] * x[i];
double normX = Math.Sqrt(ss);
// if (normX == 0.0) continue; // risky
if (Math.Abs(normX) "lt" 1.0e-12) continue;
double sign;
if (x[0] "gte" 0.0) sign = -1.0;
else sign = 1.0; // counter-intuitive
double[] u = new double[xn];
for (int i = 0; i "lt" xn; ++i)
u[i] = x[i] / (x[0] - sign * normX); // check div 0
u[0] = 1.0;
// compute scaling factor tau = 2 / (u^T * u)
double tau = -sign * (x[0] - sign * normX) / normX;
// dimensions for sub-matrices
int nRowsSubR = m - j; int nColsSubR = n - j;
int nRowsSubQ = m; int nColsSubQ = m - j;
double[] vr = new double[nColsSubR];
for (int c = 0; c "lt" nColsSubR; ++c)
{
double acc = 0.0;
for (int r = 0; r "lt" nRowsSubR; ++r)
acc += u[r] * RR[j + r][j + c];
vr[c] = acc;
}
double[] vq = new double[nRowsSubQ];
for (int r = 0; r "lt" nRowsSubQ; ++r)
{
double acc = 0.0;
for (int c = 0; c "lt" nColsSubQ; ++c)
acc += u[c] * QQ[r][j + c];
vq[r] = acc;
}
// update sub-R
for (int r = 0; r "lt" nRowsSubR; ++r)
for (int c = 0; c "lt" nColsSubR; ++c)
RR[j + r][j + c] -= tau * u[r] * vr[c];
// update sub-Q
for (int r = 0; r "lt" nRowsSubQ; ++r)
for (int c = 0; c "lt" nColsSubQ; ++c)
QQ[r][j + c] -= tau * vq[r] * u[c];
} // j
// extract QQ RR into out params
Q = MatMake(m, n);
for (int i = 0; i "lt" m; ++i)
for (int j = 0; j "lt" n; ++j)
Q[i][j] = QQ[i][j];
R = MatMake(n, n);
for (int i = 0; i "lt" n; ++i)
for (int j = 0; j "lt" n; ++j)
R[i][j] = RR[i][j];
return;
} // MatDecompQR
} // class QRHouseholder
// ========================================================
public class NearestNeighborsRegressor
{
public int nNeighbors;
public double[] weights;
public double[][] trainX;
public double[] trainY;
// ------------------------------------------------------
public NearestNeighborsRegressor(int nNeighbors)
{
this.nNeighbors = nNeighbors;
this.weights = new double[nNeighbors];
for (int k = 0; k "lt" nNeighbors; ++k)
this.weights[k] = 1.0 / nNeighbors;
this.trainX = new double[0][]; // quasi-null
this.trainY = new double[0];
}
// ------------------------------------------------------
public void Train(double[][] trainX,
double[] trainY)
{
this.trainX = trainX; // store by ref
this.trainY = trainY;
}
// ------------------------------------------------------
public double Predict(double[] x)
{
// compute distances from x to all trainX
int N = trainX.Length;
double[] dists = new double[N];
for (int i = 0; i "lt" N; ++i)
dists[i] = Distance(x, this.trainX[i]);
// determine sort order
int[] sortedIdxs = ArgSort(dists);
double sum = 0.0;
for (int k = 0; k "lt" this.nNeighbors; ++k)
{
int idx = sortedIdxs[k]; // near to far
sum += this.trainY[idx] * this.weights[k];
}
return sum;
}
// ------------------------------------------------------
private static double Distance(double[] v1, double[] v2)
{
// Euclidean distance
int n = v1.Length;
double sum = 0.0;
for (int i = 0; i "lt" n; ++i)
sum += (v1[i] - v2[i]) * (v1[i] - v2[i]);
return Math.Sqrt(sum);
}
// ------------------------------------------------------
private static int[] ArgSort(double[] values)
{
int n = values.Length;
double[] copy = new double[n];
int[] indices = new int[n];
for (int i = 0; i "lt" n; ++i)
{
copy[i] = values[i];
indices[i] = i;
}
Array.Sort(copy, indices);
return indices;
}
} // class NearestNeighborsRegression
// ========================================================
} // ns
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
Test data:
# synthetic_test_40.txt # 0.7462, 0.4006, -0.0590, 0.6543, -0.0083, 0.1935 0.8495, -0.2260, -0.0142, -0.4911, 0.7699, 0.1078 -0.2335, -0.4049, 0.4352, -0.6183, -0.7636, 0.5088 0.1810, -0.5142, 0.2465, 0.2767, -0.3449, 0.3136 -0.8650, 0.7611, -0.0801, 0.5277, -0.4922, 0.7140 -0.2358, -0.7466, -0.5115, -0.8413, -0.3943, 0.4533 0.4834, 0.2300, 0.3448, -0.9832, 0.3568, 0.1360 -0.6502, -0.6300, 0.6885, 0.9652, 0.8275, 0.3046 -0.3053, 0.5604, 0.0929, 0.6329, -0.0325, 0.4756 -0.7995, 0.0740, -0.2680, 0.2086, 0.9176, 0.4565 -0.2144, -0.2141, 0.5813, 0.2902, -0.2122, 0.4119 -0.7278, -0.0987, -0.3312, -0.5641, 0.8515, 0.4438 0.3793, 0.1976, 0.4933, 0.0839, 0.4011, 0.1905 -0.8568, 0.9573, -0.5272, 0.3212, -0.8207, 0.7415 -0.5785, 0.0056, -0.7901, -0.2223, 0.0760, 0.5551 0.0735, -0.2188, 0.3925, 0.3570, 0.3746, 0.2191 0.1230, -0.2838, 0.2262, 0.8715, 0.1938, 0.2878 0.4792, -0.9248, 0.5295, 0.0366, -0.9894, 0.3149 -0.4456, 0.0697, 0.5359, -0.8938, 0.0981, 0.3879 0.8629, -0.8505, -0.4464, 0.8385, 0.5300, 0.1769 0.1995, 0.6659, 0.7921, 0.9454, 0.9970, 0.2330 -0.0249, -0.3066, -0.2927, -0.4923, 0.8220, 0.2437 0.4513, -0.9481, -0.0770, -0.4374, -0.9421, 0.2879 -0.3405, 0.5931, -0.3507, -0.3842, 0.8562, 0.3987 0.9538, 0.0471, 0.9039, 0.7760, 0.0361, 0.1706 -0.0887, 0.2104, 0.9808, 0.5478, -0.3314, 0.4128 -0.8220, -0.6302, 0.0537, -0.1658, 0.6013, 0.4306 -0.4123, -0.2880, 0.9074, -0.0461, -0.4435, 0.5144 0.0060, 0.2867, -0.7775, 0.5161, 0.7039, 0.3599 -0.7968, -0.5484, 0.9426, -0.4308, 0.8148, 0.2979 0.7811, 0.8450, -0.6877, 0.7594, 0.2640, 0.2362 -0.6802, -0.1113, -0.8325, -0.6694, -0.6056, 0.6544 0.3821, 0.1476, 0.7466, -0.5107, 0.2592, 0.1648 0.7265, 0.9683, -0.9803, -0.4943, -0.5523, 0.2454 -0.9049, -0.9797, -0.0196, -0.9090, -0.4433, 0.6447 -0.4607, 0.1811, -0.2389, 0.4050, -0.0078, 0.5229 0.2664, -0.2932, -0.4259, -0.7336, 0.8742, 0.1834 -0.4507, 0.1029, -0.6294, -0.1158, -0.6294, 0.6081 0.8948, -0.0124, 0.9278, 0.2899, -0.0314, 0.1534 -0.1323, -0.8813, -0.0146, -0.0697, 0.6135, 0.2386
.NET Test Automation Recipes
Software Testing
SciPy Programming Succinctly
Keras Succinctly
R Programming
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Microsoft MLADS Conference
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