///<summary>
/// VIDYA
///</summary>
///<param name="pNav">Navigator</param>
///<param name="pSource">Field Source</param>
///<param name="periods">Periods</param>
///<param name="R2Scale">R2 Scale</param>
///<param name="Alias">Alias</param>
///<returns>Recordset</returns>
public Recordset VIDYA(Navigator pNav, Field pSource, int periods, double R2Scale, string Alias)
{
int Record;
LinearRegression LR = new LinearRegression();
int RecordCount = pNav.RecordCount;
Field Field1 = new Field(RecordCount, Alias);
Recordset Results = LR.Regression(pNav, pSource, periods);
const int Start = 2;
pNav.Position = Start;
for (Record = Start; Record < RecordCount + 1; Record++)
{
pNav.MovePrevious();
double PreviousValue = pSource.ValueEx(pNav.Position);
pNav.MoveNext();
double R2Scaled = Results.ValueEx("RSquared", pNav.Position) * R2Scale;
Field1.Value(pNav.Position, R2Scaled *
pSource.Value(pNav.Position) + (1 - R2Scaled) * PreviousValue);
pNav.MoveNext();
}//Record
Results.AddField(Field1);
return(Results);
}
static void RegressAtLag(CompanyObservations compObs, int lag, SqlCommand cmd, CompanyObservations.RegressionType type)
{
DoubleVector prices = compObs.GetPrices(type, compObs.Length - lag, 1);
DoubleVector laggedPrices = compObs.GetPrices(type, compObs.Length - lag, lag);
//Regress price & priceLag
LinearRegression priceRegression = new LinearRegression(new DoubleMatrix(laggedPrices), prices);
LinearRegressionAnova priceAnova = new LinearRegressionAnova(priceRegression);
DoubleMatrix companyGen = compObs.GetCompanyGenerated(type, lag);
//Regress Price and compLag
LinearRegression companyRegression = new LinearRegression(companyGen, prices);
LinearRegressionAnova companyAnova = new LinearRegressionAnova(companyRegression);
DoubleMatrix customerGen = compObs.GetCustomerGenerated(type, lag);
//Regress Price and cust lag
LinearRegression customerRegression = new LinearRegression(customerGen, prices);
LinearRegressionAnova customerAnova = new LinearRegressionAnova(customerRegression);
double priceExplain = Double.IsInfinity(priceAnova.AdjustedRsquared) ? 0 : priceAnova.AdjustedRsquared;
double companyExplain = Double.IsInfinity(companyAnova.AdjustedRsquared) ? 0 : companyAnova.AdjustedRsquared;
double customerExplain = Double.IsInfinity(customerAnova.AdjustedRsquared) ? 0 : customerAnova.AdjustedRsquared;
cmd.CommandText = $"Insert INTO RegressionResults VALUES ({compObs.CompanyID}, {lag}, {priceExplain}, {customerExplain}, {companyExplain}, {(int) type})";
cmd.ExecuteNonQuery();
}
public static IInterpolator1D RegressNotContinuous(double[] Xs, double[] Ys, int nSegments)
{
var nSamples = Xs.Length;
//var x = new double[nSegments + 1];
//var y = new double[nSegments + 1];
var samplesPerSegment = nSamples / nSegments;
var interps = new IInterpolator1D[nSegments];
var uBounds = new double[nSegments];
for (var i = 0; i < nSegments; i++)
{
var sampleXs = Xs.Skip(i * samplesPerSegment).Take(samplesPerSegment).ToArray();
var sampleYs = Ys.Skip(i * samplesPerSegment).Take(samplesPerSegment).ToArray();
var lr = LinearRegression.LinearRegressionVector(sampleXs, sampleYs);
var xLo = sampleXs.First();
var xHi = sampleXs.Last();
var yLo = lr.Alpha + lr.Beta * xLo;
var yHi = lr.Alpha + lr.Beta * xHi;
interps[i] = InterpolatorFactory.GetInterpolator(new[] { xLo, xHi }, new[] { yLo, yHi }, Interpolator1DType.Linear);
uBounds[i] = xHi;
}
uBounds[uBounds.Length - 1] = double.MaxValue;
return(new NonContinuousInterpolator(uBounds, interps));
}
public override void Init(IRepository repository, IEnumerable<string> releases)
{
base.Init(repository, releases);
double dd = repository.SelectionDSL()
.Commits().TillRevision(PredictionRelease)
.Modifications().InCommits()
.CodeBlocks().InModifications().CalculateDefectDensity(PredictionRelease);
context.SetCommits(null, PredictionRelease);
regression = new LinearRegression();
foreach (var file in GetFilesInRevision(PredictionRelease))
{
double ddForFile = repository.SelectionDSL()
.Commits().TillRevision(PredictionRelease)
.Files().IdIs(file.ID)
.Modifications().InCommits().InFiles()
.CodeBlocks().InModifications().CalculateDefectDensity(PredictionRelease);
if (ddForFile >= dd)
{
context.SetFiles(e => e.IdIs(file.ID));
regression.AddTrainingData(
GetPredictorValuesFor(context)[0],
NumberOfFixedDefectsForFile(file.ID)
);
}
}
regression.Train();
}
public void Calculate()
{
double summary = 0;
foreach (var pair in pairs)
{
var regression = new LinearRegression();
regression.Compute(pair.DeltaValues.ToDecimal(), synthIndex.ToDecimal());
pair.Weight = 1 / (1 + Math.Abs(regression.Beta.ToDouble()));
summary += pair.Weight;
}
foreach (var pair in pairs)
{
pair.Weight = pair.Weight / summary;
pair.TradeVolume = Balance * pair.Weight;
}
foreach (var pair in pairs)
{
double beta = pair.Regression.Beta.ToDouble();
double weight = 1.0 / (1.0 + Math.Abs(beta));
pair.X.TradeVolume = pair.TradeVolume * (weight * Math.Abs(beta));
pair.Y.TradeVolume = pair.TradeVolume * weight;
}
}
public void CheckRegression(LinearRegression lr)
{
Assert.AreEqual(86.7434, lr.Alpha.ToDouble(), 0.001);
Assert.AreEqual(0.0189, lr.Beta.ToDouble(), 0.001);
Assert.AreEqual(0.4164, lr.RValue.ToDouble(), 0.001);
Assert.AreEqual(0.1734, lr.RSquared.ToDouble(), 0.001);
}
/// <summary>
/// Calibrates an input image using VizieR stars catalogs.
/// </summary>
/// <param name="VizieRStars">List of VizieR stars.</param>
/// <param name="DetectedStars">List of locally detected stars.</param>
/// <param name="PositionError">Maximum position error of stars. Value in arcseconds.</param>
/// <returns>The Zero Point magnitude.</returns>
public static double Calibrate(List <StarInfo> VizieRStars, List <Star> DetectedStars, double PositionError)
{
double T = double.MaxValue, B = double.MinValue, L = double.MaxValue, R = double.MinValue;
List <Tuple <Star, StarInfo> > Pairs = new List <Tuple <Star, StarInfo> >();
foreach (Star s in DetectedStars)
{
if (s.EqCenter.Dec < T)
{
T = s.EqCenter.Dec;
}
if (s.EqCenter.Dec > B)
{
B = s.EqCenter.Dec;
}
if (s.EqCenter.RA > R)
{
R = s.EqCenter.RA;
}
if (s.EqCenter.RA < L)
{
L = s.EqCenter.RA;
}
}
QuadTree <Star> Tree = new QuadTree <Star>(10, T, B, L, R);
foreach (Star s in DetectedStars)
{
Tree.Add(s, s.EqCenter.RA, s.EqCenter.Dec);
}
foreach (StarInfo si in VizieRStars)
{
var Stars = Tree.Query(si.Coordinate.RA, si.Coordinate.Dec, Arc1Sec * PositionError);
var St2 = Tree.Query(si.Coordinate.RA, si.Coordinate.Dec, Arc1Sec * PositionError * 5);
if (St2.Count == 1 & Stars.Count == 1)
{
Pairs.Add(new Tuple <Star, StarInfo>(Stars[0], si));
}
}
if (Pairs.Count < 5)
{
throw new IndexOutOfRangeException("Could not find enough pairs for calibration.");
}
var Rpairs1 = Pairs.ToArray();
var ZPSet = Pairs.Select((x) => x.Item2.Magnitude + 2.5 * Math.Log10(x.Item1.Flux)).ToArray();
Array.Sort(ZPSet, Rpairs1);
var Rpairs2 = Rpairs1.Skip(Rpairs1.Length / 4).Take(Rpairs1.Length / 2).ToList();
LinearRegression.LinearRegressionParameters LRP = LinearRegression.ComputeLinearRegression(Rpairs2.Select((x) => Math.Log10(x.Item1.Flux)).ToArray(), Rpairs2.Select((x) => x.Item2.Magnitude).ToArray());
if (LRP.PearsonR * LRP.PearsonR < CalibMinR * CalibMinR)
{
throw new ArgumentOutOfRangeException("Could not calibrate the fluxes with enough accuracy.");
}
return(ZPSet[ZPSet.Length / 2]);
}
private IRegressionSolution CreateLinearRegressionSolution()
{
if (Content == null)
{
throw new InvalidOperationException();
}
double rmse, cvRmsError;
var problemData = (IRegressionProblemData)ProblemData.Clone();
if (!problemData.TrainingIndices.Any())
{
return(null); // don't create an LR model if the problem does not have a training set (e.g. loaded into an existing model)
}
//clear checked inputVariables
foreach (var inputVariable in problemData.InputVariables.CheckedItems)
{
problemData.InputVariables.SetItemCheckedState(inputVariable.Value, false);
}
//check inputVariables used in the symbolic regression model
var usedVariables =
Content.Model.SymbolicExpressionTree.IterateNodesPostfix().OfType <VariableTreeNode>().Select(
node => node.VariableName).Distinct();
foreach (var variable in usedVariables)
{
problemData.InputVariables.SetItemCheckedState(
problemData.InputVariables.First(x => x.Value == variable), true);
}
var solution = LinearRegression.CreateLinearRegressionSolution(problemData, out rmse, out cvRmsError);
solution.Name = "Baseline (linear subset)";
return(solution);
}
private void PlotLinearRegression(List <GPoint> points)
{
var ls = new OxyPlot.Series.LineSeries()
{
MarkerType = ShowMarker ? MarkerType.None : MarkerType.Plus,
MarkerStroke = OxyPlot.OxyColors.Blue
};
LinearFunction func;
if (LinearRegression.Regression(points.ToArray(), out func))
{
int TOTAL = 10;
double x = points.First().X;
double stepX = (points.Last().X - x) / TOTAL;
for (int i = 0; i <= TOTAL; i++)
{
double y = func.Slope * x + func.Intercept;
ls.Points.Add(new OxyPlot.DataPoint(x, y));
x += stepX;
}
ls.Title = $"Linear Regression(R: {func.CorrelationCoeff:f5})";
}
else
{
ls.Title = "Linear Regression(Failed)";
}
base.Series.Add(ls);
}
/// <summary>
/// Computes the next value of this indicator from the given state
/// </summary>
/// <param name="input">The input given to the indicator</param>
/// <returns>
/// A new value for this indicator
/// </returns>
protected override decimal ComputeNextValue(IndicatorDataPoint input)
{
_standardDeviation.Update(input);
LinearRegression.Update(input);
return(LinearRegression.Current.Value);
}
private void RunRl()
{
var list = GetAllModelForWeekday(selectedWeekday);
var takeNumber = list.Count;
var comeHomingValues =
list.OrderByDescending(u => u.Date)
.Select(z => new TimeSpan(0, int.Parse(z.Hour), int.Parse(z.Minutes), 0))
.Take(takeNumber)
.ToList();
var xs = new double[takeNumber];
var value = 0.1;
for (var i = 0; i < xs.Length; i++)
{
xs[i] = value;
value += 0.1;
}
var comeHomingHourValues =
comeHomingValues.Select(y => TimeConverter.ConvertFromTimeToDouble(y.TotalMinutes)).ToArray();
double r;
double yintercept;
double slope;
LinearRegression.Execute(xs, comeHomingHourValues, 1, takeNumber - 1, out r, out yintercept, out slope);
var predictionValue = slope * (value + 0.1) + yintercept;
_predictRL = predictionValue;
}
public void Predict()
{
if (this.model == null)
{
Debug.Log("Create model before");
return;
}
// Call lib to predict test spheres
foreach (var testSphere in testSpheres)
{
var position = testSphere.position;
double[] inputs = { position.x, position.z };
var predicted = LinearRegression.linear_model_predict_regression(this.model.Value, 2, inputs);
position = new Vector3(
position.x,
(float)predicted,
position.z
);
testSphere.position = position;
}
Debug.Log("Predicted");
}
public override void Init(IRepository repository, IEnumerable <string> releases)
{
base.Init(repository, releases);
double dd = repository.SelectionDSL()
.Commits().TillRevision(PredictionRelease)
.Modifications().InCommits()
.CodeBlocks().InModifications().CalculateDefectDensity(PredictionRelease);
context.SetCommits(null, PredictionRelease);
regression = new LinearRegression();
foreach (var file in GetFilesInRevision(PredictionRelease))
{
double ddForFile = repository.SelectionDSL()
.Commits().TillRevision(PredictionRelease)
.Files().IdIs(file.ID)
.Modifications().InCommits().InFiles()
.CodeBlocks().InModifications().CalculateDefectDensity(PredictionRelease);
if (ddForFile >= dd)
{
context.SetFiles(e => e.IdIs(file.ID));
regression.AddTrainingData(
GetPredictorValuesFor(context)[0],
NumberOfFixedDefectsForFile(file.ID)
);
}
}
regression.Train();
}
public void TestLinearRegression()
{
// Control.LinearAlgebraProvider = new MklLinearAlgebraProvider();
// a simple dataset
var x = DenseMatrix.OfArray(new double[, ] {
{ 1 }, { 2 }
});
var y = DenseVector.OfEnumerable(new double[] { 1, 2 });
var clf = new LinearRegression();
clf.Fit(x, y);
Assert.AreEqual(1.0, clf.Coef.Column(0)[0], 1E-5);
//Assert.AreEqual(0.0, clf.Intercept[0]);
Assert.IsTrue(DenseVector.OfEnumerable(new double[] { 1, 2 }).AlmostEquals(clf.Predict(x).Column(0)));
// test it also for degenerate input
x = DenseMatrix.OfArray(new double[, ] {
{ 1 }
});
y = DenseVector.OfEnumerable(new double[] { 0 });
clf = new LinearRegression(fitIntercept: false);
clf.Fit(x, y);
Assert.AreEqual(0.0, clf.Coef.Column(0)[0]);
//assert_array_almost_equal(clf.intercept_, [0])
Assert.AreEqual(0.0, clf.Predict(x).Column(0)[0]);
}
public void ParallelNSampler()
{
var prior = from a in Normal(0, 100)
from b in Normal(0, 100)
select new Param(a, b);
var smc = LinearRegression.CreateLinearRegression(prior, LinearRegression.BeachSandData).SmcStandard(5000);
var sTimer = new Stopwatch();
sTimer.Start();
var serial = from s1 in smc
from s2 in smc
from s3 in smc
select new Tuple <Samples <Param>, Samples <Param>, Samples <Param> >(s1, s2, s3);
var result = serial.SampleN(2).ToList();
sTimer.Stop();
var pTimer = new Stopwatch();
pTimer.Start();
var parallel = from s1 in Independent(smc)
from s2 in Independent(smc)
from s3 in Independent(smc)
from triple in RunIndependent(s1, s2, s3)
select triple;
var thing = parallel.SampleNParallel(2).ToList();
pTimer.Stop();
Trace.WriteLine($"parallel: {pTimer.ElapsedMilliseconds}ms, serial: {sTimer.ElapsedMilliseconds}ms");
Assert.IsTrue(pTimer.ElapsedMilliseconds < sTimer.ElapsedMilliseconds);
}
/// <summary>
/// Computes the next value of this indicator from the given state
/// </summary>
/// <param name="time"></param>
/// <param name="input">The input given to the indicator</param>
/// <returns>
/// A new value for this indicator
/// </returns>
protected override DoubleArray Forward(long time, DoubleArray input)
{
_standardDeviation.Update(time, input);
LinearRegression.Update(time, input);
return(LinearRegression.Current);
}
public void TestFitIntercept()
{
var x2 = DenseMatrix.OfArray(new[, ]
{
{ 0.38349978, 0.61650022 },
{ 0.58853682, 0.41146318 }
});
var x3 = DenseMatrix.OfArray(new[, ]
{
{ 0.27677969, 0.70693172, 0.01628859 },
{ 0.08385139, 0.20692515, 0.70922346 }
});
var y = DenseVector.OfEnumerable(new double[] { 1, 1 });
var lr2WithoutIntercept = new LinearRegression(fitIntercept: false);
lr2WithoutIntercept.Fit(x2, y);
var lr2WithIntercept = new LinearRegression(fitIntercept: true);
lr2WithIntercept.Fit(x2, y);
var lr3WithoutIntercept = new LinearRegression(fitIntercept: false);
lr3WithoutIntercept.Fit(x3, y);
var lr3WithIntercept = new LinearRegression(fitIntercept: true);
lr3WithIntercept.Fit(x3, y);
Assert.AreEqual(lr2WithIntercept.Coef.Column(0).Count,
lr2WithoutIntercept.Coef.Column(0).Count);
Assert.AreEqual(lr3WithIntercept.Coef.Column(0).Count,
lr3WithoutIntercept.Coef.Column(0).Count);
}
public void Example4a()
{
var line = new LinearRegression(table4a);
Assert.AreEqual(13.67, line.a, 0.01);
Assert.AreEqual(7.03, line.b, 0.01);
}
private IRegressionSolution CreateLinearRegressionSolution()
{
if (Content == null)
{
throw new InvalidOperationException();
}
double rmse, cvRmsError;
var problemData = (IRegressionProblemData)ProblemData.Clone();
if (!problemData.TrainingIndices.Any())
{
return(null); // don't create an LR model if the problem does not have a training set (e.g. loaded into an existing model)
}
var usedVariables = Content.Model.VariablesUsedForPrediction;
var usedDoubleVariables = usedVariables
.Where(name => problemData.Dataset.VariableHasType <double>(name))
.Distinct();
var usedFactorVariables = usedVariables
.Where(name => problemData.Dataset.VariableHasType <string>(name))
.Distinct();
// gkronber: for binary factors we actually produce a binary variable in the new dataset
// but only if the variable is not used as a full factor anyway (LR creates binary columns anyway)
var usedBinaryFactors =
Content.Model.SymbolicExpressionTree.IterateNodesPostfix().OfType <BinaryFactorVariableTreeNode>()
.Where(node => !usedFactorVariables.Contains(node.VariableName))
.Select(node => Tuple.Create(node.VariableValue, node.VariableValue));
// create a new problem and dataset
var variableNames =
usedDoubleVariables
.Concat(usedFactorVariables)
.Concat(usedBinaryFactors.Select(t => t.Item1 + "=" + t.Item2))
.Concat(new string[] { problemData.TargetVariable })
.ToArray();
var variableValues =
usedDoubleVariables.Select(name => (IList)problemData.Dataset.GetDoubleValues(name).ToList())
.Concat(usedFactorVariables.Select(name => problemData.Dataset.GetStringValues(name).ToList()))
.Concat(
// create binary variable
usedBinaryFactors.Select(t => problemData.Dataset.GetReadOnlyStringValues(t.Item1).Select(val => val == t.Item2 ? 1.0 : 0.0).ToList())
)
.Concat(new[] { problemData.Dataset.GetDoubleValues(problemData.TargetVariable).ToList() });
var newDs = new Dataset(variableNames, variableValues);
var newProblemData = new RegressionProblemData(newDs, variableNames.Take(variableNames.Length - 1), variableNames.Last());
newProblemData.TrainingPartition.Start = problemData.TrainingPartition.Start;
newProblemData.TrainingPartition.End = problemData.TrainingPartition.End;
newProblemData.TestPartition.Start = problemData.TestPartition.Start;
newProblemData.TestPartition.End = problemData.TestPartition.End;
var solution = LinearRegression.CreateLinearRegressionSolution(newProblemData, out rmse, out cvRmsError);
solution.Name = "Baseline (linear subset)";
return(solution);
}
public void Example4b()
{
var line = new LinearRegression(table4b);
Assert.AreEqual(-2.49, line.a, 0.01);
Assert.AreEqual(244.18, line.b, 0.01);
Assert.AreEqual(-0.767, line.r, 0.001);
}
private IRegressionSolution CreateLinearSolution()
{
double rmsError, cvRmsError;
var solution = LinearRegression.CreateLinearRegressionSolution((IRegressionProblemData)ProblemData.Clone(), out rmsError, out cvRmsError);
solution.Name = "Baseline (linear)";
return(solution);
}
public void PredictTest()
{
double[,] features = { { 1d, 0d }, { 1d, 1d }, { 1d, 2d }, { 1d, 3d }, { 1d, 4d } };
double[] theta = { 1d, -1d };
double[] labels = { 1d, 0d, -1d, -2d, -3d };
double[] predictions = LinearRegression.Predict(features, theta);
CollectionAssert.AreEqual(labels, predictions);
}
/// <summary>
/// Resets this indicator and all sub-indicators (StandardDeviation, LowerBand, MiddleBand, UpperBand)
/// </summary>
public override void Reset()
{
_standardDeviation.Reset();
LinearRegression.Reset();
LowerChannel.Reset();
UpperChannel.Reset();
base.Reset();
}
public void PredictCurrencyExchangeRate_ValidData_ShouldSucceed(int[] xVals, double[] yVals, int monthToPredict, double expectedValue)
{
// Act
double actualValue = LinearRegression.PredictCurrencyExchangeRate(xVals, yVals, monthToPredict);
// Assert
Assert.Equal(expectedValue, actualValue);
}
public void PredictCurrencyExchangeRate_DifferentArrayLengths_ShouldFail(int[] xVals, double[] yVals, int monthToPredict)
{
// Act
Action act = () => LinearRegression.PredictCurrencyExchangeRate(xVals, yVals, monthToPredict);
// Assert
Assert.Throws <ArgumentException>(act);
}
private static void TestLinearRegression(FeatureVector training, FeatureVector test)
{
LinearRegression lr = new LinearRegression();
LinearRegressionModel lrModel = (LinearRegressionModel)lr.Fit(training);
FeatureVector predictions = lrModel.transform(test);
PrintPredictionsAndEvaluate(predictions);
}
public void PerfectFitTest()
{
double[,] features = { { 1d, 0d }, { 1d, 1d }, { 1d, 2d }, { 1d, 3d }, { 1d, 4d } };
double[] theta = { 1d, -1d };
double[] labels = { 1d, 0d, -1d, -2d, -3d };
Assert.AreEqual(0d, LinearRegression.Cost(features, labels, theta), 0.001d);
Assert.AreEqual(0d, LinearRegression.Gradient(features, labels, theta).Sum(), 0.001d);
}
public Task <byte[]> Execute(byte[] data)
{
// prep the data
Int32 questionId = BitConverter.ToInt32(data, 0);
Console.WriteLine("Node task created with parameter: " + questionId);
return(Task.Factory.StartNew(() =>
{
// To prevent any x-threaded issues
Int32 q = questionId;
Random rnd = new Random(q);
// prep the regres algorithm
LinearRegression regres = new LinearRegression();
double[] y;
double[,] x;
double[] w; // weighting
using (SqlConnection conn = new SqlConnection(@"Data Source=kivu;Initial Catalog=StackoverflowAug2012;uid=sblackler;pwd=password"))
{
conn.Open();
var results = conn.Query <PostResult>(@"SELECT TOP 8000 id, PostScore, ViewCount FROM Posts WHERE AcceptedAnswerId IS NULL AND AnswerCount < 10 AND PostScore > (SELECT TOP 1 PostScore FROM Posts WHERE ID = @Q) ORDER BY PostScore DESC", new { Q = rnd.Next(0, 11750761) }).ToList();
y = results.Select(p => p.ID).ToArray();
Int32 i = 0;
x = new double[results.Count, results.Count];
foreach (var el in results)
{
for (Int32 j = 1; j < results.Count; j++)
{
x[i, j - 1] = (el.PostScore < 1 ? 1 : el.PostScore / el.ViewCount < 1 ? 1 : el.ViewCount) * j / 100;
}
}
}
w = new double[Math.Max(y.Length, x.Length)];
// Blank the array with the value 1
Extensions.MemSet(w, 1);
try
{
if (regres.Regress(y, x, w))
{
return BitConverter.GetBytes((int)regres.SEC[0]);
}
}
catch { return BitConverter.GetBytes(-1); }
// In case the regression fails.
return BitConverter.GetBytes(rnd.Next(0, 11750761));
}));
}
private void TestLinearRegression()
{
LinearRegression linearRegression = new LinearRegression(trainingEpochs, learningRate);
linearRegression.Train(dataX, dataY);
(float[] results, float optimalWeights, float optimalBias) = linearRegression.Predict(testX);
//analytical solution coefficientVector=(X'*X)*X'*Y where X is the inputX with ones in the first column and Y is inputY: bias=0.7988 and weight=0.2516
Assert.Equal(0.309068531, optimalWeights, 6);
Assert.Equal(0.373608261, optimalBias, 6);
}
public void WrongDataSetVariableImpactRegressionTest()
{
IRegressionProblemData problemData = LoadDefaultTowerProblem();
double rmsError;
double cvRmsError;
var solution = LinearRegression.CreateSolution(problemData, out rmsError, out cvRmsError);
solution.ProblemData = LoadDefaultMibaProblem();
RegressionSolutionVariableImpactsCalculator.CalculateImpacts(solution);
}
public void LinearRegressionModelVariableImpactMibaTest()
{
IRegressionProblemData problemData = LoadDefaultMibaProblem();
double rmsError;
double cvRmsError;
var solution = LinearRegression.CreateSolution(problemData, out rmsError, out cvRmsError);
Dictionary <string, double> expectedImpacts = GetExpectedValuesForLRMiba();
CheckDefaultAsserts(solution, expectedImpacts);
}
public void test1dLinearRegression()
{
//BOOST_MESSAGE("Testing 1d simple linear least-squares regression...");
/* Example taken from the QuantLib-User list, see posting
* Multiple linear regression/weighted regression, Boris Skorodumov */
//SavedSettings backup;
List<double> x = new InitializedList<double>(9),
y = new InitializedList<double>(9);
x[0] = 2.4; x[1] = 1.8; x[2] = 2.5; x[3] = 3.0;
x[4] = 2.1; x[5] = 1.2; x[6] = 2.0; x[7] = 2.7; x[8] = 3.6;
y[0] = 7.8; y[1] = 5.5; y[2] = 8.0; y[3] = 9.0;
y[4] = 6.5; y[5] = 4.0; y[6] = 6.3; y[7] = 8.4; y[8] = 10.2;
List<Func<double, double>> v = new List<Func<double, double>>();
v.Add(a => 1.0);
v.Add(a => a);
LinearRegression m = new LinearRegression(x, y);
const double tol = 0.0002;
double[] coeffExpected = new double[] { 0.9448, 2.6853 };
double[] errorsExpected = new double[] { 0.3654, 0.1487 };
for (int i = 0; i < 2; ++i) {
if (Math.Abs(m.standardErrors()[i] - errorsExpected[i]) > tol) {
Assert.Fail("Failed to reproduce linear regression standard errors"
+ "\n calculated: " + m.standardErrors()[i]
+ "\n expected: " + errorsExpected[i]
+ "\n tolerance: " + tol);
}
if (Math.Abs(m.coefficients()[i] - coeffExpected[i]) > tol) {
Assert.Fail("Failed to reproduce linear regression coef."
+ "\n calculated: " + m.coefficients()[i]
+ "\n expected: " + coeffExpected[i]
+ "\n tolerance: " + tol);
}
}
}
public float GetSlope(SectionPathLossCalcParam param, short[] altitudes, int nIndex)
{
int fNumber = (int) (param.MergeEdgeMaxDis / (4f * param.CalcResolution));
if (fNumber < 1)
{
fNumber = 1;
}
fNumber = Math.Min(this.Trim(fNumber, 5, 10), nIndex);
float[] a = new float[fNumber * 2];
float[] y = new float[fNumber];
int num2 = nIndex;
for (int i = 0; i < fNumber; i++)
{
a[i] = num2 * param.CalcResolution;
y[i] = altitudes[num2 - 1];
num2--;
}
float[] numArray3 = new float[2];
float[] numArray4 = new float[3];
LinearRegression regression = new LinearRegression();
MatrixOperation operation = new MatrixOperation();
regression.mvfitgn(a, y, numArray3, fNumber, 2, false);
return numArray3[1];
}
private static LinearRegression getRegression(double[] dependent_, double[] independent_)
{
var yV = new DoubleVector(dependent_);
var matrix = new DoubleMatrix(independent_.ToColumn());
var lin = new LinearRegression(obs: yV, A: matrix, addIntercept: true);
return lin;
}
public void TestRidgeVsLstsq()
{
var random = new Random(0);
// we need more samples than features
const int nSamples = 5;
const int nFeatures = 4;
var y = DenseVector.CreateRandom(nSamples, new Normal { RandomSource = random });
var x = DenseMatrix.CreateRandom(nSamples, nFeatures, new Normal { RandomSource = random });
var ridge = new RidgeRegression(alpha: 0.0, fitIntercept: false);
var ols = new LinearRegression(fitIntercept: false);
ridge.Fit(x, y);
ols.Fit(x, y);
Assert.IsTrue(ridge.Coef.AlmostEquals(ols.Coef));
ridge.Fit(x, y);
ols.Fit(x, y);
Assert.IsTrue(ridge.Coef.AlmostEquals(ols.Coef));
}
private ReturnValue Recursion(float[] valueMatrix, float[] actualLossMatrix, float[] coeMatrix, int validDataNumber, int coeNumNeedAdjust, bool isAdjustClutter)
{
ReturnValue value2 = ReturnValue.PROPADJ_SUCCESS;
if (coeNumNeedAdjust == 0)
{
return ReturnValue.PROPCOR_NOSUCESS;
}
if (validDataNumber < 10)
{
return ReturnValue.PROPCOR_LACKDATAERROR;
}
float[] numArray = new float[validDataNumber];
LinearRegression regression = new LinearRegression();
MatrixOperation operation = new MatrixOperation();
int num = 0;
try
{
num = regression.mvfitgn(valueMatrix, actualLossMatrix, coeMatrix, validDataNumber, coeNumNeedAdjust, isAdjustClutter);
}
catch (Exception exception)
{
WriteLog.Logger.Error(exception.StackTrace);
}
if (num != 0)
{
return ReturnValue.PROPCOR_NOTFIT;
}
return value2;
}
/// <summary>
/// Demonstrates linear reression in two dimensions.
/// </summary>
void LinearRegression()
{
// Set up example description
nRichDescription.Text = "A linear regression model is computed from the sample data containing random normal noise. \n\nA point is then predicted from the model with a 95% confidence interval - meaning the predicted point is expected to lie within the confidence interval 95% of the time.";
// First read in the independent (or predictor) values. This is a matrix
// with one column and a row for each amounts measurement.
DoubleVector raw_data = new DoubleVector(25, 0, 1);
DoubleMatrix measurements = new DoubleMatrix(raw_data);
// Next, read in the responses
// Build a linear polynomial and add noise for interest
RandomNumberGenerator rand = new RandGenNormal(0, noiselevel_);
Polynomial poly = new Polynomial(new DoubleVector("0, 1"));
DoubleVector responses = poly.Evaluate(raw_data) + new DoubleVector(raw_data.Length, rand); ;
// Construct a linear regression. If we want our regression to calculate a
// y-intercept we must send in true for the "addIntercept" parameter (the
// third paramameter in the constructor).
LinearRegression regression = new LinearRegression(measurements, responses, true);
DoubleVector residues = regression.Residuals;
// Use the linear regression class to make a prediction according to the model
DoubleVector xvalues = new DoubleVector("30"); // Use the model to predict the observation at 30.
Interval pi = regression.PredictionInterval(xvalues, 0.95);
// Build some data points along the regression line for display
DoubleMatrix abcissae = new DoubleMatrix(new DoubleVector(raw_data));
DoubleVector predicted_ys = regression.PredictedObservations(abcissae);
// Build the chart
SetupChartLayout("Linear Regression");
NChart chart = nChartControl1.Charts[0];
SetupChartAxes(chart);
// Set up the line series
NLineSeries line = new NLineSeries();
chart.Series.Add(line);
// tell the series to regard the X values
line.UseXValues = true;
// no data labels
line.DataLabelStyle.Visible = false;
// Set the line color
line.BorderStyle = new NStrokeStyle(2.0f, Color.Tomato);
// name data set
line.Name = "Linear Regression";
// Add the the Linear Regression line data to the line series
line.XValues.AddRange(abcissae.DataBlock.Data);
line.Values.AddRange(predicted_ys.DataBlock.Data);
// Draw the raw data points
NPointSeries point = new NPointSeries();
chart.Series.Add(point);
point.UseXValues = true;
point.DataLabelStyle.Visible = false;
// Set the point appearance properties
point.FillStyle = new NColorFillStyle(Color.SkyBlue);
point.BorderStyle = new NStrokeStyle(1.0f,Color.DarkGray);
point.PointShape = PointShape.Cross;
point.Size = new NLength(6.0f);
// Points must fit in the chart area
point.InflateMargins = true;
// Name point set
point.Name = "Observations";
// set the point data
point.Values.AddRange(responses.DataBlock.Data);
point.XValues.AddRange(measurements.DataBlock.Data);
double m = (pi.Min + pi.Max) / 2.0;
// Display the predicted value with an error bar series
NErrorBarSeries predicted_points = new NErrorBarSeries();
chart.Series.Add(predicted_points);
predicted_points.Name = "Predicted Point";
predicted_points.UseXValues = true;
predicted_points.InflateMargins = true;
predicted_points.FillStyle = new NColorFillStyle(Color.Crimson);
predicted_points.BorderStyle = new NStrokeStyle(1.0f, Color.DarkGray);
predicted_points.DataLabelStyle.Visible = false;
predicted_points.MarkerStyle.Visible = true;
predicted_points.MarkerStyle.FillStyle = new NColorFillStyle(Color.Crimson);
predicted_points.MarkerStyle.BorderStyle = new NStrokeStyle(1.0f, Color.DarkGray);
predicted_points.MarkerStyle.PointShape = PointShape.Bar;
predicted_points.MarkerStyle.Width = new NLength(5);
predicted_points.MarkerStyle.Height = new NLength(5);
predicted_points.SizeY = new NLength(5);
// Fill the data for the predicted point
predicted_points.XValues.AddRange(xvalues.DataBlock.Data);
predicted_points.Values.Add(m);
predicted_points.UpperErrorsY.Add(pi.Max - m);
predicted_points.LowerErrorsY.Add(m - pi.Min);
// Create a label to display the predicted value
NLabel label = new NLabel();
label.BoundsMode = BoundsMode.None;
label.ContentAlignment = ContentAlignment.BottomLeft;
label.Location = new NPointL(
new NLength(87, NRelativeUnit.ParentPercentage),
new NLength(3, NRelativeUnit.ParentPercentage));
label.TextStyle.TextFormat = TextFormat.XML;
label.TextStyle.FontStyle = new NFontStyle("Arial", 9);
label.TextStyle.StringFormatStyle.HorzAlign = Nevron.HorzAlign.Right;
label.TextStyle.BackplaneStyle.Visible = true;
label.TextStyle.BackplaneStyle.FillStyle = new NGradientFillStyle(GradientStyle.Horizontal, GradientVariant.Variant1, Color.FromArgb(130, 255, 255, 255), Color.FromArgb(130, 233, 233, 255));
label.TextStyle.BackplaneStyle.Shape = BackplaneShape.SmoothEdgeRectangle;
label.TextStyle.BackplaneStyle.StandardFrameStyle.InnerBorderColor = Color.White;
label.Text = "<font color = 'crimson'>" + m.ToString("0.###") + "</font> - predicted value with 95% confidence interval";
chart.ChildPanels.Add(label);
nChartControl1.Refresh();
}
/// <summary>
/// Returns a new line chart by interpolating over the given linear regression.
/// </summary>
/// <param name="lr">Linear Regression.</param>
/// <param name="predictorIndex">The predictor (independent) variable to plot on the x-axis.</param>
/// <returns>A new chart.</returns>
/// <exception cref="InvalidArgumentException">
/// Thrown if the given predictorIndex is outside the range of columns in lr.PredictorMatrix.
/// </exception>
/// <remarks>
/// The multidimensional linear regression fit is plotted projected onto the plane of the specified
/// predictor variable.
/// </remarks>
public static ChartControl ToChart( LinearRegression lr, int predictorIndex )
{
ChartControl chart = GetDefaultChart();
Update( ref chart, lr, predictorIndex );
return chart;
}
/// <summary>
/// Updates the given chart with the specified linear regression.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="lr">Linear Regression.</param>
/// <param name="predictorIndex">The predictor (independent) variable to plot on the x-axis.</param>
/// <exception cref="InvalidArgumentException">
/// Thrown if the given predictorIndex is outside the range of columns in lr.PredictorMatrix.
/// </exception>
/// <remarks>
/// The multidimensional linear regression fit is plotted projected onto the plane of the specified
/// predictor variable.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// The first two data series are replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, LinearRegression lr, int predictorIndex )
{
if( predictorIndex < 0 || predictorIndex > lr.PredictorMatrix.Cols )
{
throw new Core.IndexOutOfRangeException( predictorIndex );
}
List<string> titles = new List<string>()
{
"LinearRegression",
};
string xTitle = "Independent Variable " + predictorIndex;
string yTitle = "Dependent Variable";
// create version of predictor matrix with all other columns zeroed out
DoubleMatrix projection = new DoubleMatrix( lr.PredictorMatrix.Rows, lr.PredictorMatrix.Cols );
projection[Slice.All, predictorIndex] = lr.PredictorMatrix.Col( predictorIndex );
DoubleMatrix data = new DoubleMatrix( lr.NumberOfObservations, 3 );
data[Slice.All, 0] = lr.PredictorMatrix.Col( predictorIndex ); // x
data[Slice.All, 1] = lr.Observations; // y
data[Slice.All, 2] = lr.PredictedObservations( projection ); // y predicted
data = NMathFunctions.SortByColumn( data, 0 );
List<ChartSeries> series = new List<ChartSeries>()
{
BindXY( data.Col(0), data.Col(1), ChartSeriesType.Scatter, DefaultMarker ),
// only necessary to plot endpoints of line
BindXY( data.Col(0)[new Slice(0, 2, data.Rows - 1)], data.Col(2)[new Slice(0, 2, data.Rows - 1)], ChartSeriesType.Line, ChartSymbolShape.None )
};
series[0].Text = "Observed";
series[1].Text = "Predicted";
Update( ref chart, series, titles, xTitle, yTitle );
}
/// <summary>
/// Shows a new chart in a default form.
/// </summary>
/// <param name="lr">Linear Regression.</param>
/// <param name="predictorIndex">The predictor (independent) variable to plot on the x-axis.</param>
/// <exception cref="InvalidArgumentException">
/// Thrown if the given predictorIndex is outside the range of columns in lr.PredictorMatrix.
/// </exception>
/// <remarks>
/// The multidimensional linear regression fit is plotted projected onto the plane of the specified
/// predictor variable.
/// <br/>
/// Equivalent to:
/// <code>
/// NMathStatsChart.Show( ToChart( lr, predictorIndex ) );
/// </code>
/// </remarks>
public static void Show( LinearRegression lr, int predictorIndex )
{
Show( ToChart( lr, predictorIndex ) );
}
