protected internal override double doFirstDerivative(double xValue)
{
int lowerIndex = lowerBoundIndex(xValue, xValues);
int higherIndex = lowerIndex + 1;
RealPolynomialFunction1D[] quadFirstDerivative = quadraticsFirstDerivative_Renamed.get();
// at start of curve, or only one interval
if (lowerIndex == 0 || intervalCount == 1)
{
RealPolynomialFunction1D quadraticFirstDerivative = quadFirstDerivative[0];
double x = xValue - xValues[1];
return(quadraticFirstDerivative.applyAsDouble(x));
}
// at end of curve
if (higherIndex >= intervalCount)
{
RealPolynomialFunction1D quadraticFirstDerivative = quadFirstDerivative[intervalCount - 2];
double x = xValue - xValues[intervalCount - 1];
return(quadraticFirstDerivative.applyAsDouble(x));
}
RealPolynomialFunction1D quadratic1 = quadratics_Renamed[lowerIndex - 1];
RealPolynomialFunction1D quadratic2 = quadratics_Renamed[higherIndex - 1];
RealPolynomialFunction1D quadratic1FirstDerivative = quadFirstDerivative[lowerIndex - 1];
RealPolynomialFunction1D quadratic2FirstDerivative = quadFirstDerivative[higherIndex - 1];
double w = WEIGHT_FUNCTION.getWeight((xValues[higherIndex] - xValue) / (xValues[higherIndex] - xValues[lowerIndex]));
return(w * quadratic1FirstDerivative.applyAsDouble(xValue - xValues[lowerIndex]) + (1 - w) * quadratic2FirstDerivative.applyAsDouble(xValue - xValues[higherIndex]) + (quadratic2.applyAsDouble(xValue - xValues[higherIndex]) - quadratic1.applyAsDouble(xValue - xValues[lowerIndex])) / (xValues[higherIndex] - xValues[lowerIndex]));
}
/// <summary>
/// {@inheritDoc} </summary>
/// <exception cref="MathException"> If there are no real roots; if the Commons method could not evaluate the function; if the Commons method could not converge. </exception>
public virtual double?[] getRoots(RealPolynomialFunction1D function)
{
ArgChecker.notNull(function, "function");
try
{
Complex[] roots = ROOT_FINDER.solveAllComplex(function.Coefficients, 0);
IList <double> realRoots = new List <double>();
foreach (Complex c in roots)
{
if (DoubleMath.fuzzyEquals(c.Imaginary, 0d, EPS))
{
realRoots.Add(c.Real);
}
}
if (realRoots.Count == 0)
{
throw new MathException("Could not find any real roots");
}
return(realRoots.ToArray());
}
catch (TooManyEvaluationsException e)
{
throw new MathException(e);
}
}
//-------------------------------------------------------------------------
protected internal override double doInterpolate(double xValue)
{
// x-value is less than the x-value of the last node (lowerIndex < intervalCount)
int lowerIndex = lowerBoundIndex(xValue, xValues);
int higherIndex = lowerIndex + 1;
// at start of curve
if (lowerIndex == 0)
{
RealPolynomialFunction1D quadratic = quadratics_Renamed[0];
double x = xValue - xValues[1];
return(quadratic.applyAsDouble(x));
}
// at end of curve
if (higherIndex == intervalCount)
{
RealPolynomialFunction1D quadratic = quadratics_Renamed[intervalCount - 2];
double x = xValue - xValues[intervalCount - 1];
return(quadratic.applyAsDouble(x));
}
// normal case
RealPolynomialFunction1D quadratic1 = quadratics_Renamed[lowerIndex - 1];
RealPolynomialFunction1D quadratic2 = quadratics_Renamed[higherIndex - 1];
double w = WEIGHT_FUNCTION.getWeight((xValues[higherIndex] - xValue) / (xValues[higherIndex] - xValues[lowerIndex]));
return(w * quadratic1.applyAsDouble(xValue - xValues[lowerIndex]) + (1 - w) * quadratic2.applyAsDouble(xValue - xValues[higherIndex]));
}
//-------------------------------------------------------------------------
internal static RealPolynomialFunction1D[] quadratics(double[] x, double[] y, int intervalCount)
{
if (intervalCount == 1)
{
double a = y[1];
double b = (y[1] - y[0]) / (x[1] - x[0]);
return(new RealPolynomialFunction1D[] { new RealPolynomialFunction1D(a, b) });
}
RealPolynomialFunction1D[] quadratic = new RealPolynomialFunction1D[intervalCount - 1];
for (int i = 1; i < intervalCount; i++)
{
quadratic[i - 1] = Bound.quadratic(x, y, i);
}
return(quadratic);
}
internal static RealPolynomialFunction1D[] quadraticsFirstDerivative(double[] x, double[] y, int intervalCount)
{
if (intervalCount == 1)
{
double b = (y[1] - y[0]) / (x[1] - x[0]);
return(new RealPolynomialFunction1D[] { new RealPolynomialFunction1D(b) });
}
else
{
RealPolynomialFunction1D[] quadraticFirstDerivative = new RealPolynomialFunction1D[intervalCount - 1];
for (int i = 1; i < intervalCount; i++)
{
quadraticFirstDerivative[i - 1] = Bound.quadraticFirstDerivative(x, y, i);
}
return(quadraticFirstDerivative);
}
}
/// <summary>
/// {@inheritDoc} </summary>
/// <exception cref="IllegalArgumentException"> If the function is not a quadratic </exception>
/// <exception cref="MathException"> If the roots are not real </exception>
public virtual double?[] getRoots(RealPolynomialFunction1D function)
{
ArgChecker.notNull(function, "function");
double[] coefficients = function.Coefficients;
ArgChecker.isTrue(coefficients.Length == 3, "Function is not a quadratic");
double c = coefficients[0];
double b = coefficients[1];
double a = coefficients[2];
double discriminant = b * b - 4 * a * c;
if (discriminant < 0)
{
throw new MathException("No real roots for quadratic");
}
double q = -0.5 * (b + Math.Sign(b) * discriminant);
return(new double?[] { q / a, c / q });
}
public virtual double?[] getRoots(RealPolynomialFunction1D function)
{
ArgChecker.notNull(function, "function");
double[] coefficients = function.Coefficients;
if (coefficients.Length != 4)
{
throw new System.ArgumentException("Function is not a cubic");
}
ComplexNumber[] result = ROOT_FINDER.getRoots(function);
IList <double> reals = new List <double>();
foreach (ComplexNumber c in result)
{
if (DoubleMath.fuzzyEquals(c.Imaginary, 0d, 1e-16))
{
reals.Add(c.Real);
}
}
ArgChecker.isTrue(reals.Count > 0, "Could not find any real roots");
return(reals.toArray(EMPTY_ARRAY));
}
/// <summary>
/// Gets the polynomials.
/// </summary>
/// <param name="n"> the n value </param>
/// <param name="alpha"> the alpha value </param>
/// <returns> the result </returns>
public virtual DoubleFunction1D[] getPolynomials(int n, double alpha)
{
ArgChecker.isTrue(n >= 0);
DoubleFunction1D[] polynomials = new DoubleFunction1D[n + 1];
for (int i = 0; i <= n; i++)
{
if (i == 0)
{
polynomials[i] = One;
}
else if (i == 1)
{
polynomials[i] = new RealPolynomialFunction1D(new double[] { 1 + alpha, -1 });
}
else
{
polynomials[i] = (polynomials[i - 1].multiply(2.0 * i + alpha - 1).subtract(polynomials[i - 1].multiply(X)).subtract(polynomials[i - 2].multiply((i - 1.0 + alpha))).divide(i));
}
}
return(polynomials);
}
/// <summary>
/// {@inheritDoc} </summary>
/// <exception cref="IllegalArgumentException"> If the function is not cubic </exception>
public virtual ComplexNumber[] getRoots(RealPolynomialFunction1D function)
{
ArgChecker.notNull(function, "function");
double[] coefficients = function.Coefficients;
ArgChecker.isTrue(coefficients.Length == 4, "Function is not a cubic");
double divisor = coefficients[3];
double a = coefficients[2] / divisor;
double b = coefficients[1] / divisor;
double c = coefficients[0] / divisor;
double aSq = a * a;
double q = (aSq - 3 * b) / 9;
double r = (2 * a * aSq - 9 * a * b + 27 * c) / 54;
double rSq = r * r;
double qCb = q * q * q;
double constant = a / 3;
if (rSq < qCb)
{
double mult = -2 * Math.Sqrt(q);
double theta = Math.Acos(r / Math.Sqrt(qCb));
return(new ComplexNumber[]
{
new ComplexNumber(mult * Math.Cos(theta / 3) - constant, 0),
new ComplexNumber(mult * Math.Cos((theta + TWO_PI) / 3) - constant, 0),
new ComplexNumber(mult * Math.Cos((theta - TWO_PI) / 3) - constant, 0)
});
}
double s = -Math.Sign(r) * Math.cbrt(Math.Abs(r) + Math.Sqrt(rSq - qCb));
double t = DoubleMath.fuzzyEquals(s, 0d, 1e-16) ? 0 : q / s;
double sum = s + t;
double real = -0.5 * sum - constant;
double imaginary = Math.Sqrt(3) * (s - t) / 2;
return(new ComplexNumber[]
{
new ComplexNumber(sum - constant, 0),
new ComplexNumber(real, imaginary),
new ComplexNumber(real, -imaginary)
});
}
/// <summary>
/// Calculates polynomials. </summary>
/// <param name="n"> the n value </param>
/// <param name="alpha"> the alpha value </param>
/// <param name="beta"> the beta value </param>
/// <returns> the result </returns>
public virtual DoubleFunction1D[] getPolynomials(int n, double alpha, double beta)
{
ArgChecker.isTrue(n >= 0);
DoubleFunction1D[] polynomials = new DoubleFunction1D[n + 1];
for (int i = 0; i <= n; i++)
{
if (i == 0)
{
polynomials[i] = One;
}
else if (i == 1)
{
polynomials[i] = new RealPolynomialFunction1D(new double[] { (alpha - beta) / 2, (alpha + beta + 2) / 2 });
}
else
{
int j = i - 1;
polynomials[i] = (polynomials[j].multiply(getB(alpha, beta, j)).add(polynomials[j].multiply(X).multiply(getC(alpha, beta, j)).add(polynomials[j - 1].multiply(getD(alpha, beta, j))))).divide(getA(alpha, beta, j));
}
}
return(polynomials);
}
//JAVA TO C# CONVERTER TODO TASK: Most Java annotations will not have direct .NET equivalent attributes:
//ORIGINAL LINE: @Test public void testAlpha2()
public virtual void testAlpha2()
{
const int n = 14;
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final com.opengamma.strata.collect.tuple.Pair<com.opengamma.strata.math.impl.function.DoubleFunction1D, com.opengamma.strata.math.impl.function.DoubleFunction1D>[] polynomialAndDerivative1 = LAGUERRE.getPolynomialsAndFirstDerivative(n);
Pair <DoubleFunction1D, DoubleFunction1D>[] polynomialAndDerivative1 = LAGUERRE.getPolynomialsAndFirstDerivative(n);
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final com.opengamma.strata.collect.tuple.Pair<com.opengamma.strata.math.impl.function.DoubleFunction1D, com.opengamma.strata.math.impl.function.DoubleFunction1D>[] polynomialAndDerivative2 = LAGUERRE.getPolynomialsAndFirstDerivative(n, 0);
Pair <DoubleFunction1D, DoubleFunction1D>[] polynomialAndDerivative2 = LAGUERRE.getPolynomialsAndFirstDerivative(n, 0);
for (int i = 0; i < n; i++)
{
assertTrue(polynomialAndDerivative1[i].First is RealPolynomialFunction1D);
assertTrue(polynomialAndDerivative2[i].First is RealPolynomialFunction1D);
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final com.opengamma.strata.math.impl.function.RealPolynomialFunction1D first = (com.opengamma.strata.math.impl.function.RealPolynomialFunction1D) polynomialAndDerivative1[i].getFirst();
RealPolynomialFunction1D first = (RealPolynomialFunction1D)polynomialAndDerivative1[i].First;
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final com.opengamma.strata.math.impl.function.RealPolynomialFunction1D second = (com.opengamma.strata.math.impl.function.RealPolynomialFunction1D) polynomialAndDerivative2[i].getFirst();
RealPolynomialFunction1D second = (RealPolynomialFunction1D)polynomialAndDerivative2[i].First;
assertEquals(first, second);
}
}
/// <summary>
/// Checks coefficients of polynomial f(x) are recovered and residuals, { y_i -f(x_i) }, are accurate
/// </summary>
public virtual void PolynomialFunctionRecoverTest()
{
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final PolynomialsLeastSquaresFitter regObj = new PolynomialsLeastSquaresFitter();
PolynomialsLeastSquaresFitter regObj = new PolynomialsLeastSquaresFitter();
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final double[] coeff = new double[] {3.4, 5.6, 1.0, -4.0 };
double[] coeff = new double[] { 3.4, 5.6, 1.0, -4.0 };
DoubleFunction1D func = new RealPolynomialFunction1D(coeff);
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final int degree = coeff.length - 1;
int degree = coeff.Length - 1;
const int nPts = 7;
double[] xValues = new double[nPts];
double[] yValues = new double[nPts];
for (int i = 0; i < nPts; ++i)
{
xValues[i] = -5.0 + 10 * i / (nPts - 1);
yValues[i] = func.applyAsDouble(xValues[i]);
}
double[] yValuesNorm = new double[nPts];
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final double mean = _meanCal.apply(xValues);
double mean = _meanCal.apply(xValues);
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final double std = _stdCal.apply(xValues);
double std = _stdCal.apply(xValues);
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final double ratio = mean / std;
double ratio = mean / std;
for (int i = 0; i < nPts; ++i)
{
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final double tmp = xValues[i] / std - ratio;
double tmp = xValues[i] / std - ratio;
yValuesNorm[i] = func.applyAsDouble(tmp);
}
/// <summary>
/// Tests for regress(..)
/// </summary>
LeastSquaresRegressionResult result = regObj.regress(xValues, yValues, degree);
double[] coeffResult = result.Betas;
for (int i = 0; i < degree + 1; ++i)
{
assertEquals(coeff[i], coeffResult[i], EPS * Math.Abs(coeff[i]));
}
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final double[] residuals = result.getResiduals();
double[] residuals = result.Residuals;
func = new RealPolynomialFunction1D(coeffResult);
double[] yValuesFit = new double[nPts];
for (int i = 0; i < nPts; ++i)
{
yValuesFit[i] = func.applyAsDouble(xValues[i]);
}
for (int i = 0; i < nPts; ++i)
{
assertEquals(Math.Abs(yValuesFit[i] - yValues[i]), 0.0, Math.Abs(yValues[i]) * EPS);
}
for (int i = 0; i < nPts; ++i)
{
assertEquals(Math.Abs(yValuesFit[i] - yValues[i]), Math.Abs(residuals[i]), Math.Abs(yValues[i]) * EPS);
}
double sum = 0.0;
for (int i = 0; i < nPts; ++i)
{
sum += residuals[i] * residuals[i];
}
sum = Math.Sqrt(sum);
/// <summary>
/// Tests for regressVerbose(.., false)
/// </summary>
PolynomialsLeastSquaresFitterResult resultVer = regObj.regressVerbose(xValues, yValues, degree, false);
coeffResult = resultVer.Coeff;
func = new RealPolynomialFunction1D(coeffResult);
for (int i = 0; i < nPts; ++i)
{
yValuesFit[i] = func.applyAsDouble(xValues[i]);
}
assertEquals(nPts - (degree + 1), resultVer.Dof, 0);
for (int i = 0; i < degree + 1; ++i)
{
assertEquals(coeff[i], coeffResult[i], EPS * Math.Abs(coeff[i]));
}
for (int i = 0; i < nPts; ++i)
{
assertEquals(Math.Abs(yValuesFit[i] - yValues[i]), 0.0, Math.Abs(yValues[i]) * EPS);
}
assertEquals(sum, resultVer.DiffNorm, EPS);
/// <summary>
/// Tests for regressVerbose(.., true)
/// </summary>
PolynomialsLeastSquaresFitterResult resultNorm = regObj.regressVerbose(xValues, yValuesNorm, degree, true);
coeffResult = resultNorm.Coeff;
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final double[] meanAndStd = resultNorm.getMeanAndStd();
double[] meanAndStd = resultNorm.MeanAndStd;
assertEquals(nPts - (degree + 1), resultNorm.Dof, 0);
assertEquals(mean, meanAndStd[0], EPS);
assertEquals(std, meanAndStd[1], EPS);
for (int i = 0; i < degree + 1; ++i)
{
assertEquals(coeff[i], coeffResult[i], EPS * Math.Abs(coeff[i]));
}
func = new RealPolynomialFunction1D(coeffResult);
for (int i = 0; i < nPts; ++i)
{
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final double tmp = xValues[i] / std - ratio;
double tmp = xValues[i] / std - ratio;
yValuesFit[i] = func.applyAsDouble(tmp);
}
for (int i = 0; i < nPts; ++i)
{
assertEquals(Math.Abs(yValuesFit[i] - yValuesNorm[i]), 0.0, Math.Abs(yValuesNorm[i]) * EPS);
}
sum = 0.0;
for (int i = 0; i < nPts; ++i)
{
sum += (yValuesFit[i] - yValuesNorm[i]) * (yValuesFit[i] - yValuesNorm[i]);
}
sum = Math.Sqrt(sum);
assertEquals(sum, resultNorm.DiffNorm, EPS);
}