public void FitsAtArbitraryPointsWithMaple(double t, double x, double maxAbsoluteError)
{
IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x);
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
double interpolatedValue;
double secondDerivative;
interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
}
public void FitsAtArbitraryPointsWithMaple(double t, double x, double maxAbsoluteError)
{
IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x);
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
double interpolatedValue;
double secondDerivative;
interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
}
public void FitsAtSamplePoints()
{
IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x);
for (int i = 0; i < _x.Length; i++)
{
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
double interpolatedValue;
double secondDerivative;
interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative);
Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i);
}
}
public void FitsAtSamplePoints()
{
IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x);
for (int i = 0; i < _x.Length; i++)
{
Assert.AreEqual(_x[i], interpolation.Interpolate(_t[i]), "A Exact Point " + i);
double interpolatedValue;
double secondDerivative;
interpolation.Differentiate(_t[i], out interpolatedValue, out secondDerivative);
Assert.AreEqual(_x[i], interpolatedValue, "B Exact Point " + i);
}
}
public void FitsAtArbitraryPointsWithMaple(
[Values(0.1, 0.4, 1.1, 3.2, 4.5, 10.0, -10.0)] double t,
[Values(.57225, 1.884, 3.0314166666666666667, 1.034666666666666667, 6.28125, 277.5, -1010.8333333333333333)] double x,
[Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-12)] double maxAbsoluteError)
{
IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x);
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
double interpolatedValue;
double secondDerivative;
interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
}
public void FitsAtArbitraryPointsWithMaple(
[Values(0.1, 0.4, 1.1, 3.2, 4.5, 10.0, -10.0)] double t,
[Values(.57225, 1.884, 3.0314166666666666667, 1.034666666666666667, 6.28125, 277.5, -1010.8333333333333333)] double x,
[Values(1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-15, 1e-12)] double maxAbsoluteError)
{
IInterpolation interpolation = new NevillePolynomialInterpolation(_t, _x);
Assert.AreEqual(x, interpolation.Interpolate(t), maxAbsoluteError, "Interpolation at {0}", t);
double interpolatedValue;
double secondDerivative;
interpolation.Differentiate(t, out interpolatedValue, out secondDerivative);
Assert.AreEqual(x, interpolatedValue, maxAbsoluteError, "Interpolation as by-product of differentiation at {0}", t);
}
private DenseVector GradOfEvaluatingValueRidder(Func <DenseVector, double> inputFunction,
DenseVector dvCurrentParametersPoint,
DenseVector dvPreviousParametersIncrement, out DenseVector dvNewParametersIncrement, double maxRelativeError = 0.005d)
{
DenseVector dvCurrentParametersIncrement = dvPreviousParametersIncrement.Copy() * 2.0d;
Func <DenseVector, double> theFunction = inputFunction;
double maxRelPartialDerivAboveMin = 1000.0d;
for (int i = 0; i < dvCurrentParametersIncrement.Count; i++)
{
if (Math.Abs(dvCurrentParametersIncrement[i]) / dvParametersScale[i] < 1.0e-2)
{
dvCurrentParametersIncrement[i] = dvParametersScale[i] * 1.0e-2;
}
else if (Math.Abs(dvCurrentParametersIncrement[i]) / dvParametersScale[i] > 1.0e+2)
{
dvCurrentParametersIncrement[i] = dvParametersScale[i];
}
}
DenseVector grad = DenseVector.Create(dvCurrentParametersPoint.Count, (index) =>
{
DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
(i => (i == index) ? (dvCurrentParametersIncrement[i]) : (0.0d)));
return((theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
theFunction(dvCurrentParametersPoint - dvPartialParametersIncrement)) / (2.0d * dvPartialParametersIncrement.Sum()));
});
DenseVector gradHalfed = DenseVector.Create(dvCurrentParametersPoint.Count, (index) =>
{
DenseVector dvPartialParametersIncrementHalfed = DenseVector.Create(dvCurrentParametersIncrement.Count,
(i => (i == index) ? (dvCurrentParametersIncrement[i] / 2.0d) : (0.0d)));
return((theFunction(dvCurrentParametersPoint + dvPartialParametersIncrementHalfed) -
theFunction(dvCurrentParametersPoint - dvPartialParametersIncrementHalfed)) / (2.0d * dvPartialParametersIncrementHalfed.Sum()));
});
double relativeError = (grad - gradHalfed).Abs() / grad.Abs();
for (int varIndex = 0; varIndex < dvCurrentParametersIncrement.Count; varIndex++)
{
double partialRelativeError = relativeError;
double currentVarIncrement = dvCurrentParametersIncrement[varIndex];
List <Tuple <double, double, int> > lTplRelErrAndPartDeriv = new List <Tuple <double, double, int> >();
DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
(i => (i == varIndex) ? (dvCurrentParametersIncrement[i]) : (0.0d)));
List <DenseVector> dvParametersPointsToDetermineDerivative = new List <DenseVector>();
dvParametersPointsToDetermineDerivative.Add(dvCurrentParametersPoint - dvPartialParametersIncrement);
dvParametersPointsToDetermineDerivative.Add(dvCurrentParametersPoint + dvPartialParametersIncrement);
NevillePolynomialInterpolation interpolator = new NevillePolynomialInterpolation(
dvParametersPointsToDetermineDerivative.ConvertAll <double>(dv => dv[varIndex]).ToArray(),
dvParametersPointsToDetermineDerivative.ConvertAll <double>(dv => theFunction(dv)).ToArray());
double prevPartialDeriv = interpolator.Differentiate(dvCurrentParametersPoint[varIndex]);
int iNumberOfPointsBetween = 0;
while (partialRelativeError > maxRelativeError)
{
iNumberOfPointsBetween += 2;
List <DenseVector> dvCurrParametersPoints = new List <DenseVector>();
dvCurrParametersPoints.InsertRange(0, dvParametersPointsToDetermineDerivative);
for (int i = 1; i <= iNumberOfPointsBetween; i++)
{
dvCurrParametersPoints.Add(dvParametersPointsToDetermineDerivative[0] +
(dvParametersPointsToDetermineDerivative[1] -
dvParametersPointsToDetermineDerivative[0]) / (i + 1));
}
dvCurrParametersPoints.Sort(
(dv1, dv2) => (dv1[varIndex] < dv2[varIndex]) ? (-1) : (1));
NevillePolynomialInterpolation currInterpolator = new NevillePolynomialInterpolation(
dvCurrParametersPoints.ConvertAll <double>(dv => dv[varIndex]).ToArray(),
dvCurrParametersPoints.ConvertAll <double>(dv => theFunction(dv)).ToArray());
double currPartialDeriv = currInterpolator.Differentiate(dvCurrentParametersPoint[varIndex]);
#region // OBSOLETE
//currentVarIncrement = currentVarIncrement / 2.0d;
//if (Math.Abs(currentVarIncrement) / dvParametersScale[varIndex] < 1.0e-20)
//{
// currentVarIncrement = currentVarIncrement * 2.0d;
// break;
//}
//else if (Math.Abs(currentVarIncrement) / dvParametersScale[varIndex] > 1.0e+20)
//{
// currentVarIncrement = currentVarIncrement / 2.0d;
// break;
//}
//DenseVector gradPartial = DenseVector.Create(dvCurrentParametersPoint.Count, new Func<int, double>((index) =>
//{
// if (index != varIndex) return 0.0d;
// DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
// (i => (i == index) ? (currentVarIncrement) : (0.0d)));
// return (theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
// theFunction(dvCurrentParametersPoint)) / currentVarIncrement;
//}));
//
//DenseVector gradPartialHalfed = DenseVector.Create(dvCurrentParametersPoint.Count, new Func<int, double>((index) =>
//{
// if (index != varIndex) return 0.0d;
// DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
// (i => (i == index) ? (currentVarIncrement / 2.0d) : (0.0d)));
// return (theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
// theFunction(dvCurrentParametersPoint)) / (currentVarIncrement / 2.0d);
//}));
//double gradPartialModule = gradPartial.Abs();
//double gradPartialHalfedModule = gradPartialHalfed.Abs();
//if ((gradPartialModule == 0.0d) || (gradPartialHalfedModule == 0.0d))
//{
// currentVarIncrement = currentVarIncrement * 2.0d;
// break;
//}
// (gradPartial - gradPartialHalfed).Abs() / gradPartial.Abs();
#endregion // OBSOLETE
partialRelativeError = Math.Abs((currPartialDeriv - prevPartialDeriv) / prevPartialDeriv);
prevPartialDeriv = currPartialDeriv;
dvCurrentParametersIncrement[varIndex] = currentVarIncrement / (iNumberOfPointsBetween + 2);
lTplRelErrAndPartDeriv.Add(new Tuple <double, double, int>(partialRelativeError, currPartialDeriv, iNumberOfPointsBetween));
if (partialRelativeError / lTplRelErrAndPartDeriv.Min(tpl => tpl.Item1) > maxRelPartialDerivAboveMin)
{
prevPartialDeriv = lTplRelErrAndPartDeriv.Min(tpl => tpl.Item2);
dvCurrentParametersIncrement[varIndex] = currentVarIncrement / (lTplRelErrAndPartDeriv.Min(tpl => tpl.Item3) + 2);
break;
}
if (SelfWorker != null)
{
if (SelfWorker.CancellationPending)
{
break;
}
}
}
grad[varIndex] = prevPartialDeriv;
}
#region // OBSOLETE
//grad = DenseVector.Create(dvCurrentParametersPoint.Count, new Func<int, double>((index) =>
//{
// DenseVector dvPartialParametersIncrement = DenseVector.Create(dvCurrentParametersIncrement.Count,
// (i => (i == index) ? (dvCurrentParametersIncrement[i]) : (0.0d)));
// return (theFunction(dvCurrentParametersPoint + dvPartialParametersIncrement) -
// theFunction(dvCurrentParametersPoint - dvPartialParametersIncrement)) / (2.0d*dvPartialParametersIncrement.Sum());
//}));
#endregion // OBSOLETE
dvNewParametersIncrement = DenseVector.OfEnumerable(dvCurrentParametersIncrement);
dvNewParametersIncrement = (grad / grad.Abs()) * dvNewParametersIncrement.Abs();
return(grad);
}
