public void FitDataToLinearFunctionTest()
{
// create a data set from a linear combination of sine and cosine
Interval r = Interval.FromEndpoints(-4.0, 6.0);
double[] c = new double[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
Func <double, double> fv = delegate(double x) {
return(2.0 * Math.Cos(x) + 1.0 * Math.Sin(x));
};
Func <double, double> fu = delegate(double x) {
return(0.1 + 0.1 * Math.Abs(x));
};
UncertainMeasurementSample set = CreateDataSet(r, fv, fu, 20, 2);
// fit the data set to a linear combination of sine and cosine
Func <double, double>[] fs = new Func <double, double>[]
{ delegate(double x) { return(Math.Cos(x)); }, delegate(double x) { return(Math.Sin(x)); } };
FitResult result = set.FitToLinearFunction(fs);
// the fit should be right right dimension
Assert.IsTrue(result.Dimension == 2);
// the coefficients should match
Console.WriteLine(result.Parameter(0));
Console.WriteLine(result.Parameter(1));
Assert.IsTrue(result.Parameter(0).ConfidenceInterval(0.95).ClosedContains(2.0));
Assert.IsTrue(result.Parameter(1).ConfidenceInterval(0.95).ClosedContains(1.0));
// diagonal covarainces should match errors
Assert.IsTrue(TestUtilities.IsNearlyEqual(Math.Sqrt(result.Covariance(0, 0)), result.Parameter(0).Uncertainty));
Assert.IsTrue(TestUtilities.IsNearlyEqual(Math.Sqrt(result.Covariance(1, 1)), result.Parameter(1).Uncertainty));
}
public void NormalFitCovariances()
{
NormalDistribution N = new NormalDistribution(-1.0, 2.0);
// Create a bivariate sample to hold our fitted best mu and sigma values
// so we can determine their covariance as well as their means and variances
BivariateSample parameters = new BivariateSample();
MultivariateSample covariances = new MultivariateSample(3);
// A bunch of times, create a normal sample
for (int i = 0; i < 128; i++)
{
// We use small samples so the variation in mu and sigma will be more substantial.
Sample s = TestUtilities.CreateSample(N, 8, i);
// Fit each sample to a normal distribution
FitResult fit = NormalDistribution.FitToSample(s);
// and record the mu and sigma values from the fit into our bivariate sample
parameters.Add(fit.Parameter(0).Value, fit.Parameter(1).Value);
// also record the claimed covariances among these parameters
covariances.Add(fit.Covariance(0, 0), fit.Covariance(1, 1), fit.Covariance(0, 1));
}
// the mean fit values should agree with the population distribution
Assert.IsTrue(parameters.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(N.Mean));
Assert.IsTrue(parameters.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(N.StandardDeviation));
// but also the covariances of those fit values should agree with the claimed covariances
Assert.IsTrue(parameters.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(covariances.Column(0).Mean));
Assert.IsTrue(parameters.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(covariances.Column(1).Mean));
Assert.IsTrue(parameters.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(covariances.Column(2).Mean));
}
public void FitDataToProportionalityTest()
{
Interval r = Interval.FromEndpoints(0.0, 0.1);
Func <double, double> fv = delegate(double x) {
return(0.5 * x);
};
Func <double, double> fu = delegate(double x) {
return(0.02);
};
UncertainMeasurementSample set = CreateDataSet(r, fv, fu, 20);
// fit to proportionality
FitResult prop = set.FitToProportionality();
Assert.IsTrue(prop.Dimension == 1);
Assert.IsTrue(prop.Parameter(0).ConfidenceInterval(0.95).ClosedContains(0.5));
Assert.IsTrue(prop.GoodnessOfFit.LeftProbability < 0.95);
// fit to line
FitResult line = set.FitToLine();
Assert.IsTrue(line.Dimension == 2);
// line's intercept should be compatible with zero and slope with proportionality constant
Assert.IsTrue(line.Parameter(0).ConfidenceInterval(0.95).ClosedContains(0.0));
Assert.IsTrue(line.Parameter(1).ConfidenceInterval(0.95).ClosedContains(prop.Parameter(0).Value));
// the fit should be better, but not too much better
Assert.IsTrue(line.GoodnessOfFit.Statistic < prop.GoodnessOfFit.Statistic);
}
public void ExponentialFitUncertainty()
{
// check that the uncertainty in reported fit parameters is actually meaningful
// it should be the standard deviation of fit parameter values in a sample of many fits
// define a population distribution
ExponentialDistribution distribution = new ExponentialDistribution(4.0);
// draw a lot of samples from it; fit each sample and
// record the reported parameter value and error of each
Sample values = new Sample();
Sample uncertainties = new Sample();
for (int i = 0; i < 128; i++)
{
Sample sample = SampleTest.CreateSample(distribution, 8, i);
FitResult fit = ExponentialDistribution.FitToSample(sample);
UncertainValue lambda = fit.Parameter(0);
values.Add(lambda.Value);
uncertainties.Add(lambda.Uncertainty);
}
// the reported values should agree with the source distribution
Assert.IsTrue(values.PopulationMean.ConfidenceInterval(0.95).ClosedContains(distribution.Mean));
// the reported errors should agree with the standard deviation of the reported parameters
Assert.IsTrue(values.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(uncertainties.Mean));
}
public void FitDataToFunctionTest()
{
// create a data set from a nonlinear function
/*
* Interval r = Interval.FromEndpoints(-3.0, 5.0);
* double[] c = new double[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
* Function<double, double> fv = delegate(double x) {
* return (3.0 * Math.Cos(2.0 * Math.PI * x / 2.0 - 1.0));
* };
* Function<double, double> fu = delegate(double x) {
* return (0.1 + 0.1 * Math.Abs(x));
* };
* DataSet set = CreateDataSet(r, fv, fu, 20, 2);
*/
UncertainMeasurementSample set = new UncertainMeasurementSample();
set.Add(new UncertainMeasurement <double>(1.0, 1.0, 0.1));
set.Add(new UncertainMeasurement <double>(2.0, 0.7, 0.1));
set.Add(new UncertainMeasurement <double>(3.0, 0.0, 0.1));
set.Add(new UncertainMeasurement <double>(4.0, -0.7, 0.1));
set.Add(new UncertainMeasurement <double>(5.0, -1.0, 0.1));
set.Add(new UncertainMeasurement <double>(6.0, -0.7, 0.1));
set.Add(new UncertainMeasurement <double>(7.0, 0.0, 0.1));
set.Add(new UncertainMeasurement <double>(8.0, 0.7, 0.1));
set.Add(new UncertainMeasurement <double>(9.0, 1.0, 0.1));
// fit it to a parameterized fit function
/*
* Function<double[], double, double> ff = delegate(double[] p, double x) {
* return (p[0] * Math.Cos(2.0 * Math.PI / p[1] + p[2]));
* };
*/
Func <double[], double, double> ff = delegate(double[] p, double x) {
//Console.WriteLine(" p[0]={0}, x={1}", p[0], x);
return(p[1] * Math.Cos(x / p[0] + p[2]));
//return (x / p[0]);
};
FitResult fit = set.FitToFunction(ff, new double[] { 1.3, 1.1, 0.1 });
Console.WriteLine(fit.Parameter(0));
Console.WriteLine(fit.Parameter(1));
Console.WriteLine(fit.Parameter(2));
}
public void NormalFit()
{
// pick mu >> sigma so that we get no negative values;
// otherwise the attempt to fit to an exponential will fail
ContinuousDistribution distribution = new NormalDistribution(6.0, 2.0);
Sample sample = SampleTest.CreateSample(distribution, 100);
// fit to normal should be good
FitResult nfit = NormalDistribution.FitToSample(sample);
Assert.IsTrue(nfit.GoodnessOfFit.Probability > 0.05);
Assert.IsTrue(nfit.Parameter(0).ConfidenceInterval(0.95).ClosedContains(distribution.Mean));
Assert.IsTrue(nfit.Parameter(1).ConfidenceInterval(0.95).ClosedContains(distribution.StandardDeviation));
// fit to exponential should be bad
FitResult efit = ExponentialDistribution.FitToSample(sample);
Assert.IsTrue(efit.GoodnessOfFit.Probability < 0.05);
}
public void Bug7953()
{
// Fitting this sample to a Weibull caused a NonconvergenceException in the root finder that was used inside the fit method.
// The underlying problem was that our equation to solve involved x^k and k ~ 2000 and (~12)^(~2000) overflows double
// so all the quantities became Infinity and the root-finder never converged. We changed the algorithm to operate on
// w = log x - <log x> which keeps quantities much smaller.
Sample sample = new Sample(
12.824, 12.855, 12.861, 12.862, 12.863,
12.864, 12.865, 12.866, 12.866, 12.866,
12.867, 12.867, 12.868, 12.868, 12.870,
12.871, 12.871, 12.871, 12.871, 12.872,
12.876, 12.878, 12.879, 12.879, 12.881
);
FitResult result = WeibullDistribution.FitToSample(sample);
Console.WriteLine("{0} {1}", result.Parameter(0), result.Parameter(1));
Console.WriteLine(result.GoodnessOfFit.RightProbability);
}
public void FitDataToLineTest()
{
Interval r = Interval.FromEndpoints(0.0, 10.0);
Func <double, double> fv = delegate(double x) {
return(2.0 * x - 1.0);
};
Func <double, double> fu = delegate(double x) {
return(1.0 + x);
};
UncertainMeasurementSample data = CreateDataSet(r, fv, fu, 20);
// sanity check the data set
Assert.IsTrue(data.Count == 20);
// fit to a line
FitResult line = data.FitToLine();
Assert.IsTrue(line.Dimension == 2);
Assert.IsTrue(line.Parameter(0).ConfidenceInterval(0.95).ClosedContains(-1.0));
Assert.IsTrue(line.Parameter(1).ConfidenceInterval(0.95).ClosedContains(2.0));
Assert.IsTrue(line.GoodnessOfFit.LeftProbability < 0.95);
// correlation coefficient should be related to covariance as expected
Assert.IsTrue(TestUtilities.IsNearlyEqual(line.CorrelationCoefficient(0, 1), line.Covariance(0, 1) / line.Parameter(0).Uncertainty / line.Parameter(1).Uncertainty));
// fit to a 1st order polynomial and make sure it agrees
FitResult poly = data.FitToPolynomial(1);
Assert.IsTrue(poly.Dimension == 2);
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.Parameters, line.Parameters));
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.CovarianceMatrix, line.CovarianceMatrix));
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.GoodnessOfFit.Statistic, line.GoodnessOfFit.Statistic));
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.GoodnessOfFit.LeftProbability, line.GoodnessOfFit.LeftProbability));
Assert.IsTrue(TestUtilities.IsNearlyEqual(poly.GoodnessOfFit.RightProbability, line.GoodnessOfFit.RightProbability));
// fit to a constant; the result should be poor
FitResult constant = data.FitToConstant();
Assert.IsTrue(constant.GoodnessOfFit.LeftProbability > 0.95);
}
public void FitToFunctionPolynomialCompatibilityTest()
{
// specify a cubic function
Interval r = Interval.FromEndpoints(-10.0, 10.0);
Func <double, double> fv = delegate(double x) {
return(0.0 - 1.0 * x + 2.0 * x * x - 3.0 * x * x * x);
};
Func <double, double> fu = delegate(double x) {
return(1.0 + 0.5 * Math.Cos(x));
};
// create a data set from it
UncertainMeasurementSample set = CreateDataSet(r, fv, fu, 60);
// fit it to a cubic polynomial
FitResult pFit = set.FitToPolynomial(3);
// fit it to a cubic polynomaial
Func <double[], double, double> ff = delegate(double[] p, double x) {
return(p[0] + p[1] * x + p[2] * x * x + p[3] * x * x * x);
};
FitResult fFit = set.FitToFunction(ff, new double[] { 0, 0, 0, 0 });
// the fits should agree
Console.WriteLine("{0} ?= {1}", pFit.GoodnessOfFit.Statistic, fFit.GoodnessOfFit.Statistic);
for (int i = 0; i < pFit.Dimension; i++)
{
Console.WriteLine("{0} ?= {1}", pFit.Parameter(i), fFit.Parameter(i));
Assert.IsTrue(pFit.Parameter(i).ConfidenceInterval(0.01).ClosedContains(fFit.Parameter(i).Value));
}
// dimension
Assert.IsTrue(pFit.Dimension == fFit.Dimension);
// chi squared
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.GoodnessOfFit.Statistic, fFit.GoodnessOfFit.Statistic, Math.Sqrt(TestUtilities.TargetPrecision)));
// don't demand super-high precision agreement of parameters and covariance matrix
// parameters
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.Parameters, fFit.Parameters, Math.Pow(TestUtilities.TargetPrecision, 0.3)));
// covariance
Assert.IsTrue(TestUtilities.IsNearlyEqual(pFit.CovarianceMatrix, fFit.CovarianceMatrix, Math.Pow(TestUtilities.TargetPrecision, 0.3)));
}
public void FitDataToPolynomialTest()
{
Interval r = Interval.FromEndpoints(-10.0, 10.0);
double[] c = new double[] { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
Func <double, double> fv = delegate(double x) {
double f = 0.0;
for (int i = c.Length - 1; i >= 0; i--)
{
f = f * x + c[i];
}
return(f);
};
Func <double, double> fu = delegate(double x) {
return(1.0 + 0.5 * Math.Cos(x));
};
UncertainMeasurementSample set = CreateDataSet(r, fv, fu, 50);
Assert.IsTrue(set.Count == 50);
// fit to an appropriate polynomial
FitResult poly = set.FitToPolynomial(5);
// the coefficients should match
for (int i = 0; i < poly.Dimension; i++)
{
Assert.IsTrue(poly.Parameter(i).ConfidenceInterval(0.95).ClosedContains(c[i]));
}
// the fit should be good
Console.WriteLine(poly.GoodnessOfFit.LeftProbability);
Assert.IsTrue(poly.GoodnessOfFit.LeftProbability < 0.95);
// fit to a lower order polynomial
FitResult low = set.FitToPolynomial(4);
// the fit should be bad
Assert.IsTrue(low.GoodnessOfFit.Statistic > poly.GoodnessOfFit.Statistic);
Assert.IsTrue(low.GoodnessOfFit.LeftProbability > 0.95);
// fit to a higher order polynomial
FitResult high = set.FitToPolynomial(6);
// the higher order coefficients should be compatible with zero
Assert.IsTrue(high.Parameter(6).ConfidenceInterval(0.95).ClosedContains(0.0));
// the fit should be better, but not too much better
Assert.IsTrue(high.GoodnessOfFit.Statistic < poly.GoodnessOfFit.Statistic);
}
public void ExponentialFit()
{
ExponentialDistribution distribution = new ExponentialDistribution(5.0);
Sample sample = SampleTest.CreateSample(distribution, 100);
// fit to normal should be bad
FitResult nfit = NormalDistribution.FitToSample(sample);
Assert.IsTrue(nfit.GoodnessOfFit.Probability < 0.05);
// fit to exponential should be good
FitResult efit = ExponentialDistribution.FitToSample(sample);
Assert.IsTrue(efit.GoodnessOfFit.Probability > 0.05);
Assert.IsTrue(efit.Parameter(0).ConfidenceInterval(0.95).ClosedContains(distribution.Mean));
}
public void Bug6162()
{
// When UncertianMeasurementSample.FitToPolynomial used Cholesky inversion of (A^T A), this inversion
// would fail when roundoff errors would made the matrix non-positive-definite. We have now changed
// to QR decomposition, which is more robust.
//real data
double[] X_axis = new double[] { 40270.65625, 40270.6569444444, 40270.6576388888, 40270.6583333332, 40270.6590277776,
40270.659722222, 40270.6604166669, 40270.6611111113, 40270.6618055557, 40270.6625000001 };
double[] Y_axis = new double[] { 246.824996948242, 246.850006103516, 245.875, 246.225006103516, 246.975006103516,
247.024993896484, 246.949996948242, 246.875, 247.5, 247.100006103516 };
UncertainMeasurementSample DataSet = new UncertainMeasurementSample();
for (int i = 0; i < 10; i++)
{
DataSet.Add(X_axis[i], Y_axis[i], 1);
}
//for (int i = 0; i < 10; i++) DataSet.Add(X_axis[i] - 40270.0, Y_axis[i] - 247.0, 1);
FitResult DataFit = DataSet.FitToPolynomial(3);
for (int i = 0; i < DataFit.Dimension; i++)
{
Console.WriteLine("a" + i.ToString() + " = " + DataFit.Parameter(i).Value);
}
BivariateSample bs = new BivariateSample();
for (int i = 0; i < 10; i++)
{
bs.Add(X_axis[i], Y_axis[i]);
}
FitResult bsFit = bs.PolynomialRegression(3);
for (int i = 0; i < bsFit.Dimension; i++)
{
Console.WriteLine(bsFit.Parameter(i));
}
}
public void MultivariateLinearRegressionTest()
{
// define model y = a + b0 * x0 + b1 * x1 + noise
double a = 1.0;
double b0 = -2.0;
double b1 = 3.0;
Distribution noise = new NormalDistribution(0.0, 10.0);
// draw a sample from the model
Random rng = new Random(1);
MultivariateSample sample = new MultivariateSample(3);
for (int i = 0; i < 100; i++)
{
double x0 = -10.0 + 20.0 * rng.NextDouble();
double x1 = -10.0 + 20.0 * rng.NextDouble();
double eps = noise.InverseLeftProbability(rng.NextDouble());
double y = a + b0 * x0 + b1 * x1 + eps;
sample.Add(x0, x1, y);
}
// do a linear regression fit on the model
FitResult result = sample.LinearRegression(2);
// the result should have the appropriate dimension
Assert.IsTrue(result.Dimension == 3);
// the result should be significant
Console.WriteLine("{0} {1}", result.GoodnessOfFit.Statistic, result.GoodnessOfFit.LeftProbability);
Assert.IsTrue(result.GoodnessOfFit.LeftProbability > 0.95);
// the parameters should match the model
Console.WriteLine(result.Parameter(0));
Assert.IsTrue(result.Parameter(0).ConfidenceInterval(0.90).ClosedContains(b0));
Console.WriteLine(result.Parameter(1));
Assert.IsTrue(result.Parameter(1).ConfidenceInterval(0.90).ClosedContains(b1));
Console.WriteLine(result.Parameter(2));
Assert.IsTrue(result.Parameter(2).ConfidenceInterval(0.90).ClosedContains(a));
}
//only compute after drives are achieved
public void ComputeMotionEffortCoefs(DriveParams[] driveParams)
{
//using (StreamWriter sw = new StreamWriter("regressionCoefs.txt")) {
double param = 0;
for (int coefInd = 0; coefInd < _motionEffortCoefs[0].Length; coefInd++)
{
MultivariateSample efforts = new MultivariateSample(5); //4 efforts + 1 coefficient
for (int i = 0; i < 32; i++)
{
if (coefInd == (int)MotionCoef.Speed)
{
param = driveParams[i].Speed;
}
else if (coefInd == (int)MotionCoef.V0)
{
param = driveParams[i].V0;
}
else if (coefInd == (int)MotionCoef.V1)
{
param = driveParams[i].V1;
}
else if (coefInd == (int)MotionCoef.Ti)
{
param = driveParams[i].Ti;
}
else if (coefInd == (int)MotionCoef.Texp)
{
param = driveParams[i].Texp;
}
else if (coefInd == (int)MotionCoef.TVal)
{
param = driveParams[i].Tval;
}
else if (coefInd == (int)MotionCoef.T0)
{
param = driveParams[i].T0;
}
else if (coefInd == (int)MotionCoef.T1)
{
param = driveParams[i].T1;
}
else if (coefInd == (int)MotionCoef.HrMag)
{
param = Mathf.Abs(driveParams[i].HrMag);
}
else if (coefInd == (int)MotionCoef.HSign)
{
param = driveParams[i].HSign;
}
else if (coefInd == (int)MotionCoef.HfMag)
{
param = driveParams[i].HfMag;
}
else if (coefInd == (int)MotionCoef.SquashMag)
{
param = driveParams[i].SquashMag;
}
else if (coefInd == (int)MotionCoef.WbMag)
{
param = driveParams[i].WbMag;
}
else if (coefInd == (int)MotionCoef.WxMag)
{
param = driveParams[i].WxMag;
}
else if (coefInd == (int)MotionCoef.WtMag)
{
param = driveParams[i].WtMag;
}
else if (coefInd == (int)MotionCoef.WfMag)
{
param = driveParams[i].WfMag;
}
else if (coefInd == (int)MotionCoef.EtMag)
{
param = driveParams[i].EtMag;
}
else if (coefInd == (int)MotionCoef.EfMag)
{
param = driveParams[i].EfMag;
}
else if (coefInd == (int)MotionCoef.DMag)
{
param = driveParams[i].DMag;
}
else if (coefInd == (int)MotionCoef.TrMag)
{
param = driveParams[i].TrMag;
}
else if (coefInd == (int)MotionCoef.TfMag)
{
param = driveParams[i].TfMag;
}
else if (coefInd == (int)MotionCoef.EncSpr0)
{
param = driveParams[i].EncSpr0;
}
else if (coefInd == (int)MotionCoef.SinRis0)
{
param = driveParams[i].SinRis0;
}
else if (coefInd == (int)MotionCoef.RetAdv0)
{
param = driveParams[i].RetAdv0;
}
else if (coefInd == (int)MotionCoef.EncSpr1)
{
param = driveParams[i].EncSpr1;
}
else if (coefInd == (int)MotionCoef.SinRis1)
{
param = driveParams[i].SinRis1;
}
else if (coefInd == (int)MotionCoef.RetAdv1)
{
param = driveParams[i].RetAdv1;
}
else if (coefInd == (int)MotionCoef.EncSpr2)
{
param = driveParams[i].EncSpr2;
}
else if (coefInd == (int)MotionCoef.SinRis2)
{
param = driveParams[i].SinRis2;
}
else if (coefInd == (int)MotionCoef.RetAdv2)
{
param = driveParams[i].RetAdv2;
}
else if (coefInd == (int)MotionCoef.Continuity)
{
param = driveParams[i].Continuity;
}
else if (coefInd == (int)MotionCoef.Arm0X)
{
param = driveParams[i].Arm[0].x;
}
else if (coefInd == (int)MotionCoef.Arm0Y)
{
param = driveParams[i].Arm[0].y;
}
else if (coefInd == (int)MotionCoef.Arm0Z)
{
param = driveParams[i].Arm[0].z;
}
else if (coefInd == (int)MotionCoef.Arm1X)
{
param = driveParams[i].Arm[1].x;
}
else if (coefInd == (int)MotionCoef.Arm1Y)
{
param = driveParams[i].Arm[1].y;
}
else if (coefInd == (int)MotionCoef.Arm1Z)
{
param = driveParams[i].Arm[1].z;
}
else if (coefInd == (int)MotionCoef.ShapeTi)
{
param = driveParams[i].ShapeTi;
}
else if (coefInd == (int)MotionCoef.ExtraGoal)
{
param = driveParams[i].ExtraGoal;
}
else if (coefInd == (int)MotionCoef.UseCurveKeys)
{
param = driveParams[i].UseCurveKeys;
}
else if (coefInd == (int)MotionCoef.FixedTarget)
{
param = driveParams[i].FixedTarget;
}
else if (coefInd == (int)MotionCoef.SquashF)
{
param = driveParams[i].SquashF;
}
else if (coefInd == (int)MotionCoef.GoalThreshold)
{
param = driveParams[i].GoalThreshold;
}
efforts.Add(param, _xRange[i][0], _xRange[i][1], _xRange[i][2], _xRange[i][3]);
}
FitResult regression = efforts.LinearRegression(0); //keep motion parameter fixed
//intercept, space, time, weight, flow coefficients
for (int i = 0; i < 5; i++)
{
_motionEffortCoefs[i][coefInd] = (float)regression.Parameter(i).Value;
}
// sw.WriteLine(_motionEffortCoefs[0][coefInd] + "\t" + _motionEffortCoefs[1][coefInd] + "\t" +
// _motionEffortCoefs[2][coefInd] + "\t" + _motionEffortCoefs[3][coefInd] + "\t" +
// _motionEffortCoefs[4][coefInd]);
// }
}
}
public void BivariateLinearRegression()
{
// do a set of logistic regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as returned
Random rng = new Random(314159);
// define logistic parameters
double a0 = 2.0; double b0 = -1.0;
// keep track of sample of returned a and b fit parameters
BivariateSample ps = new BivariateSample();
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
double caa = 0.0;
double cbb = 0.0;
double cab = 0.0;
// also keep track of test statistics
Sample fs = new Sample();
// do 100 fits
for (int k = 0; k < 100; k++)
{
// we should be able to draw x's from any distribution; noise should be drawn from a normal distribution
Distribution xd = new LogisticDistribution();
Distribution nd = new NormalDistribution(0.0, 2.0);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int i = 0; i < 25; i++)
{
double x = xd.GetRandomValue(rng);
double y = a0 + b0 * x + nd.GetRandomValue(rng);
s.Add(x, y);
}
// do the regression
FitResult r = s.LinearRegression();
// record best fit parameters
double a = r.Parameter(0).Value;
double b = r.Parameter(1).Value;
ps.Add(a, b);
// record estimated covariances
caa += r.Covariance(0, 0);
cbb += r.Covariance(1, 1);
cab += r.Covariance(0, 1);
// record the fit statistic
fs.Add(r.GoodnessOfFit.Statistic);
Console.WriteLine("F={0}", r.GoodnessOfFit.Statistic);
}
caa /= ps.Count;
cbb /= ps.Count;
cab /= ps.Count;
// check that mean parameter estimates are what they should be: the underlying population parameters
Assert.IsTrue(ps.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(a0));
Assert.IsTrue(ps.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(b0));
Console.WriteLine("{0} {1}", caa, ps.X.PopulationVariance);
Console.WriteLine("{0} {1}", cbb, ps.Y.PopulationVariance);
// check that parameter covarainces are what they should be: the reported covariance estimates
Assert.IsTrue(ps.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(caa));
Assert.IsTrue(ps.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cbb));
Assert.IsTrue(ps.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cab));
// check that F is distributed as it should be
Console.WriteLine(fs.KolmogorovSmirnovTest(new FisherDistribution(2, 48)).LeftProbability);
}
public void LinearLogisticRegression()
{
// do a set of logistic regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as returned
Random rng = new Random(314159);
// define logistic parameters
double a0 = 1.0; double b0 = -1.0 / 2.0;
//double a0 = -0.5; double b0 = 2.0;
// keep track of sample of returned a and b fit parameters
BivariateSample ps = new BivariateSample();
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
double caa = 0.0;
double cbb = 0.0;
double cab = 0.0;
// do 50 fits
for (int k = 0; k < 50; k++)
{
Console.WriteLine("k={0}", k);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int i = 0; i < 50; i++)
{
double x = 2.0 * rng.NextDouble() - 1.0;
double ez = Math.Exp(a0 + b0 * x);
double P = ez / (1.0 + ez);
if (rng.NextDouble() < P)
{
s.Add(x, 1.0);
}
else
{
s.Add(x, 0.0);
}
}
//if (k != 27) continue;
// do the regression
FitResult r = s.LinearLogisticRegression();
// record best fit parameters
double a = r.Parameter(0).Value;
double b = r.Parameter(1).Value;
ps.Add(a, b);
Console.WriteLine("{0}, {1}", a, b);
// record estimated covariances
caa += r.Covariance(0, 0);
cbb += r.Covariance(1, 1);
cab += r.Covariance(0, 1);
}
caa /= ps.Count;
cbb /= ps.Count;
cab /= ps.Count;
// check that mean parameter estimates are what they should be: the underlying population parameters
Assert.IsTrue(ps.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(a0));
Assert.IsTrue(ps.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(b0));
// check that parameter covarainces are what they should be: the reported covariance estimates
Assert.IsTrue(ps.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(caa));
Assert.IsTrue(ps.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cbb));
Assert.IsTrue(ps.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cab));
}