HansenTesseralLinear.java
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package org.orekit.propagation.semianalytical.dsst.utilities.hansen;
import org.hipparchus.analysis.differentiation.Gradient;
import org.hipparchus.analysis.polynomials.PolynomialFunction;
import org.hipparchus.util.FastMath;
import org.orekit.propagation.semianalytical.dsst.utilities.NewcombOperators;
/**
* Hansen coefficients K(t,n,s) for t!=0 and n < 0.
* <p>
* Implements Collins 4-236 or Danielson 2.7.3-(9) for Hansen Coefficients and
* Collins 4-240 for derivatives. The recursions are transformed into
* composition of linear transformations to obtain the associated polynomials
* for coefficients and their derivatives - see Petre's paper
*
* @author Petre Bazavan
* @author Lucian Barbulescu
*/
public class HansenTesseralLinear {
/** The number of coefficients that will be computed with a set of roots. */
private static final int SLICE = 10;
/**
* The first vector of polynomials associated to Hansen coefficients and
* derivatives.
*/
private PolynomialFunction[][] mpvec;
/** The second vector of polynomials associated only to derivatives. */
private PolynomialFunction[][] mpvecDeriv;
/** The Hansen coefficients used as roots. */
private final double[][] hansenRoot;
/** The derivatives of the Hansen coefficients used as roots. */
private final double[][] hansenDerivRoot;
/** The minimum value for the order. */
private final int Nmin;
/** The index of the initial condition, Petre's paper. */
private final int N0;
/** The number of slices needed to compute the coefficients. */
private final int numSlices;
/**
* The offset used to identify the polynomial that corresponds to a negative.
* value of n in the internal array that starts at 0
*/
private final int offset;
/** The objects used to calculate initial data by means of Newcomb operators. */
private final HansenCoefficientsBySeries[] hansenInit;
/**
* Constructor.
*
* @param nMax the maximum (absolute) value of n parameter
* @param s s parameter
* @param j j parameter
* @param n0 the minimum (absolute) value of n
* @param maxHansen maximum power of e2 in Hansen expansion
*/
public HansenTesseralLinear(final int nMax, final int s, final int j, final int n0, final int maxHansen) {
//Initialize the fields
this.offset = nMax + 1;
this.Nmin = -nMax - 1;
this.N0 = -n0 - 4;
//Ensure that only the needed terms are computed
final int maxRoots = FastMath.min(4, N0 - Nmin + 4);
this.hansenInit = new HansenCoefficientsBySeries[maxRoots];
for (int i = 0; i < maxRoots; i++) {
this.hansenInit[i] = new HansenCoefficientsBySeries(N0 - i + 3, s, j, maxHansen);
}
// The first 4 values are computed with series. No linear combination is needed.
final int size = N0 - Nmin;
this.numSlices = (int) FastMath.max(FastMath.ceil(((double) size) / SLICE), 1);
hansenRoot = new double[numSlices][4];
hansenDerivRoot = new double[numSlices][4];
if (size > 0) {
mpvec = new PolynomialFunction[size][];
mpvecDeriv = new PolynomialFunction[size][];
// Prepare the database of the associated polynomials
HansenUtilities.generateTesseralPolynomials(N0, Nmin, offset, SLICE, j, s,
mpvec, mpvecDeriv);
}
}
/**
* Compute the values for the first four coefficients and their derivatives by means of series.
*
* @param e2 e²
* @param chi Χ
* @param chi2 Χ²
*/
public void computeInitValues(final double e2, final double chi, final double chi2) {
// compute the values for n, n+1, n+2 and n+3 by series
// See Danielson 2.7.3-(10)
//Ensure that only the needed terms are computed
final int maxRoots = FastMath.min(4, N0 - Nmin + 4);
for (int i = 0; i < maxRoots; i++) {
final Gradient hansenKernel = hansenInit[i].getValueGradient(e2, chi, chi2);
this.hansenRoot[0][i] = hansenKernel.getValue();
this.hansenDerivRoot[0][i] = hansenKernel.getPartialDerivative(0);
}
for (int i = 1; i < numSlices; i++) {
for (int k = 0; k < 4; k++) {
final PolynomialFunction[] mv = mpvec[N0 - (i * SLICE) - k + 3 + offset];
final PolynomialFunction[] sv = mpvecDeriv[N0 - (i * SLICE) - k + 3 + offset];
hansenDerivRoot[i][k] = mv[3].value(chi) * hansenDerivRoot[i - 1][3] +
mv[2].value(chi) * hansenDerivRoot[i - 1][2] +
mv[1].value(chi) * hansenDerivRoot[i - 1][1] +
mv[0].value(chi) * hansenDerivRoot[i - 1][0] +
sv[3].value(chi) * hansenRoot[i - 1][3] +
sv[2].value(chi) * hansenRoot[i - 1][2] +
sv[1].value(chi) * hansenRoot[i - 1][1] +
sv[0].value(chi) * hansenRoot[i - 1][0];
hansenRoot[i][k] = mv[3].value(chi) * hansenRoot[i - 1][3] +
mv[2].value(chi) * hansenRoot[i - 1][2] +
mv[1].value(chi) * hansenRoot[i - 1][1] +
mv[0].value(chi) * hansenRoot[i - 1][0];
}
}
}
/**
* Compute the value of the Hansen coefficient K<sub>j</sub><sup>-n-1, s</sup>.
*
* @param mnm1 -n-1
* @param chi χ
* @return the coefficient K<sub>j</sub><sup>-n-1, s</sup>
*/
public double getValue(final int mnm1, final double chi) {
//Compute n
final int n = -mnm1 - 1;
//Compute the potential slice
int sliceNo = (n + N0 + 4) / SLICE;
if (sliceNo < numSlices) {
//Compute the index within the slice
final int indexInSlice = (n + N0 + 4) % SLICE;
//Check if a root must be returned
if (indexInSlice <= 3) {
return hansenRoot[sliceNo][indexInSlice];
}
} else {
//the value was a potential root for a slice, but that slice was not required
//Decrease the slice number
sliceNo--;
}
// Computes the coefficient by linear transformation
// Danielson 2.7.3-(9) or Collins 4-236 and Petre's paper
final PolynomialFunction[] v = mpvec[mnm1 + offset];
return v[3].value(chi) * hansenRoot[sliceNo][3] +
v[2].value(chi) * hansenRoot[sliceNo][2] +
v[1].value(chi) * hansenRoot[sliceNo][1] +
v[0].value(chi) * hansenRoot[sliceNo][0];
}
/**
* Compute the value of the derivative dK<sub>j</sub><sup>-n-1, s</sup> / de².
*
* @param mnm1 -n-1
* @param chi χ
* @return the derivative dK<sub>j</sub><sup>-n-1, s</sup> / de²
*/
public double getDerivative(final int mnm1, final double chi) {
//Compute n
final int n = -mnm1 - 1;
//Compute the potential slice
int sliceNo = (n + N0 + 4) / SLICE;
if (sliceNo < numSlices) {
//Compute the index within the slice
final int indexInSlice = (n + N0 + 4) % SLICE;
//Check if a root must be returned
if (indexInSlice <= 3) {
return hansenDerivRoot[sliceNo][indexInSlice];
}
} else {
//the value was a potential root for a slice, but that slice was not required
//Decrease the slice number
sliceNo--;
}
// Computes the coefficient by linear transformation
// Danielson 2.7.3-(9) or Collins 4-236 and Petre's paper
final PolynomialFunction[] v = mpvec[mnm1 + this.offset];
final PolynomialFunction[] vv = mpvecDeriv[mnm1 + this.offset];
return v[3].value(chi) * hansenDerivRoot[sliceNo][3] +
v[2].value(chi) * hansenDerivRoot[sliceNo][2] +
v[1].value(chi) * hansenDerivRoot[sliceNo][1] +
v[0].value(chi) * hansenDerivRoot[sliceNo][0] +
vv[3].value(chi) * hansenRoot[sliceNo][3] +
vv[2].value(chi) * hansenRoot[sliceNo][2] +
vv[1].value(chi) * hansenRoot[sliceNo][1] +
vv[0].value(chi) * hansenRoot[sliceNo][0];
}
/**
* Compute a Hansen coefficient with series.
* <p>
* This class implements the computation of the Hansen kernels
* through a power series in e² and that is using
* modified Newcomb operators. The reference formulae can be found
* in Danielson 2.7.3-10 and 3.3-5
* </p>
*/
private static class HansenCoefficientsBySeries {
/** -n-1 coefficient. */
private final int mnm1;
/** s coefficient. */
private final int s;
/** j coefficient. */
private final int j;
/** Max power in e² for the Newcomb's series expansion. */
private final int maxNewcomb;
/** Polynomial representing the serie. */
private final PolynomialFunction polynomial;
/**
* Class constructor.
*
* @param mnm1 -n-1 value
* @param s s value
* @param j j value
* @param maxHansen max power of e² in series expansion
*/
HansenCoefficientsBySeries(final int mnm1, final int s,
final int j, final int maxHansen) {
this.mnm1 = mnm1;
this.s = s;
this.j = j;
this.maxNewcomb = maxHansen;
this.polynomial = generatePolynomial();
}
/** Computes the value of Hansen kernel and its derivative at e².
* <p>
* The formulae applied are described in Danielson 2.7.3-10 and
* 3.3-5
* </p>
* @param e2 e²
* @param chi Χ
* @param chi2 Χ²
* @return the value of the Hansen coefficient and its derivative for e²
*/
public Gradient getValueGradient(final double e2, final double chi, final double chi2) {
//Estimation of the serie expansion at e2
final Gradient serie = polynomial.value(Gradient.variable(1, 0, e2));
final double value = FastMath.pow(chi2, -mnm1 - 1) * serie.getValue() / chi;
final double coef = -(mnm1 + 1.5);
final double derivative = coef * chi2 * value +
FastMath.pow(chi2, -mnm1 - 1) * serie.getPartialDerivative(0) / chi;
return new Gradient(value, derivative);
}
/** Generate the serie expansion in e².
* <p>
* Generate the series expansion in e² used in the formulation
* of the Hansen kernel (see Danielson 2.7.3-10):
* Σ Y<sup>ns</sup><sub>α+a,α+b</sub>
* *e<sup>2α</sup>
* </p>
* @return polynomial representing the power serie expansion
*/
private PolynomialFunction generatePolynomial() {
// Initialization
final int aHT = FastMath.max(j - s, 0);
final int bHT = FastMath.max(s - j, 0);
final double[] coefficients = new double[maxNewcomb + 1];
//Loop for getting the Newcomb operators
for (int alphaHT = 0; alphaHT <= maxNewcomb; alphaHT++) {
coefficients[alphaHT] =
NewcombOperators.getValue(alphaHT + aHT, alphaHT + bHT, mnm1, s);
}
//Creation of the polynomial
return new PolynomialFunction(coefficients);
}
}
}