/**
* Get a hashCode for the complex number. Any {@code Double.NaN} value in real or imaginary part
* produces the same hash code {@code 7}.
*
* @return a hash code value for this object.
*/
@Override
public int hashCode() {
if (isNaN) {
return 7;
}
return 37 * (17 * MathUtils.hash(imaginary) + MathUtils.hash(real));
}
/**
* Copies source to dest.
*
* <p>Neither source nor dest can be null.
*
* @param source Product to copy
* @param dest Product to copy to
* @throws NullArgumentException if either source or dest is null
*/
public static void copy(Product source, Product dest) throws NullArgumentException {
MathUtils.checkNotNull(source);
MathUtils.checkNotNull(dest);
dest.setData(source.getDataRef());
dest.n = source.n;
dest.value = source.value;
}
/**
* Copies source to dest.
*
* <p>Neither source nor dest can be null.
*
* @param source Mean to copy
* @param dest Mean to copy to
* @throws NullArgumentException if either source or dest is null
*/
public static void copy(Mean source, Mean dest) throws NullArgumentException {
MathUtils.checkNotNull(source);
MathUtils.checkNotNull(dest);
dest.setData(source.getDataRef());
dest.incMoment = source.incMoment;
dest.moment = source.moment.copy();
}
/**
* Copies source to dest.
*
* <p>Neither source nor dest can be null.
*
* @param source Percentile to copy
* @param dest Percentile to copy to
* @throws NullArgumentException if either source or dest is null
*/
public static void copy(Percentile source, Percentile dest) throws NullArgumentException {
MathUtils.checkNotNull(source);
MathUtils.checkNotNull(dest);
dest.setData(source.getDataRef());
if (source.cachedPivots != null) {
System.arraycopy(source.cachedPivots, 0, dest.cachedPivots, 0, source.cachedPivots.length);
}
dest.quantile = source.quantile;
}
/* 116: */
/* 117: */ public static void copy(Kurtosis source, Kurtosis dest)
/* 118: */ throws NullArgumentException
/* 119: */ {
/* 120:218 */ MathUtils.checkNotNull(source);
/* 121:219 */ MathUtils.checkNotNull(dest);
/* 122:220 */ dest.setData(source.getDataRef());
/* 123:221 */ dest.moment = source.moment.copy();
/* 124:222 */ dest.incMoment = source.incMoment;
/* 125: */ }
/**
* Performs all dimension checks on the parameters of {@link #solve(RealLinearOperator,
* RealVector, RealVector) solve} and {@link #solveInPlace(RealLinearOperator, RealVector,
* RealVector) solveInPlace}, and throws an exception if one of the checks fails.
*
* @param a the linear operator A of the system
* @param b the right-hand side vector
* @param x0 the initial guess of the solution
* @throws NullArgumentException if one of the parameters is {@code null}
* @throws NonSquareOperatorException if {@code a} is not square
* @throws DimensionMismatchException if {@code b} or {@code x0} have dimensions inconsistent with
* {@code a}
*/
protected static void checkParameters(
final RealLinearOperator a, final RealVector b, final RealVector x0)
throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException {
MathUtils.checkNotNull(a);
MathUtils.checkNotNull(b);
MathUtils.checkNotNull(x0);
if (a.getRowDimension() != a.getColumnDimension()) {
throw new NonSquareOperatorException(a.getRowDimension(), a.getColumnDimension());
}
if (b.getDimension() != a.getRowDimension()) {
throw new DimensionMismatchException(b.getDimension(), a.getRowDimension());
}
if (x0.getDimension() != a.getColumnDimension()) {
throw new DimensionMismatchException(x0.getDimension(), a.getColumnDimension());
}
}
/** {@inheritDoc} */
public void setSubMatrix(final double[][] subMatrix, final int row, final int column)
throws NoDataException, OutOfRangeException, DimensionMismatchException,
NullArgumentException {
MathUtils.checkNotNull(subMatrix);
final int nRows = subMatrix.length;
if (nRows == 0) {
throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_ROW);
}
final int nCols = subMatrix[0].length;
if (nCols == 0) {
throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_COLUMN);
}
for (int r = 1; r < nRows; ++r) {
if (subMatrix[r].length != nCols) {
throw new DimensionMismatchException(nCols, subMatrix[r].length);
}
}
MatrixUtils.checkRowIndex(this, row);
MatrixUtils.checkColumnIndex(this, column);
MatrixUtils.checkRowIndex(this, nRows + row - 1);
MatrixUtils.checkColumnIndex(this, nCols + column - 1);
for (int i = 0; i < nRows; ++i) {
for (int j = 0; j < nCols; ++j) {
setEntry(row + i, column + j, subMatrix[i][j]);
}
}
}
/**
* Returns a {@code Complex} whose value is {@code (this / divisor)}. Implements the definitional
* formula
*
* <pre>
* <code>
* a + bi ac + bd + (bc - ad)i
* ----------- = -------------------------
* c + di c<sup>2</sup> + d<sup>2</sup>
* </code>
* </pre>
*
* but uses <a href="http://doi.acm.org/10.1145/1039813.1039814">prescaling of operands</a> to
* limit the effects of overflows and underflows in the computation. <br>
* {@code Infinite} and {@code NaN} values are handled according to the following rules, applied
* in the order presented:
*
* <ul>
* <li>If either {@code this} or {@code divisor} has a {@code NaN} value in either part, {@link
* #NaN} is returned.
* <li>If {@code divisor} equals {@link #ZERO}, {@link #NaN} is returned.
* <li>If {@code this} and {@code divisor} are both infinite, {@link #NaN} is returned.
* <li>If {@code this} is finite (i.e., has no {@code Infinite} or {@code NaN} parts) and {@code
* divisor} is infinite (one or both parts infinite), {@link #ZERO} is returned.
* <li>If {@code this} is infinite and {@code divisor} is finite, {@code NaN} values are
* returned in the parts of the result if the {@link java.lang.Double} rules applied to the
* definitional formula force {@code NaN} results.
* </ul>
*
* @param divisor Value by which this {@code Complex} is to be divided.
* @return {@code this / divisor}.
* @throws NullArgumentException if {@code divisor} is {@code null}.
*/
public Complex divide(Complex divisor) throws NullArgumentException {
MathUtils.checkNotNull(divisor);
if (isNaN || divisor.isNaN) {
return NaN;
}
final double c = divisor.getReal();
final double d = divisor.getImaginary();
if (c == 0.0 && d == 0.0) {
return NaN;
}
if (divisor.isInfinite() && !isInfinite()) {
return ZERO;
}
if (FastMath.abs(c) < FastMath.abs(d)) {
double q = c / d;
double denominator = c * q + d;
return createComplex(
(real * q + imaginary) / denominator, (imaginary * q - real) / denominator);
} else {
double q = d / c;
double denominator = d * q + c;
return createComplex(
(imaginary * q + real) / denominator, (imaginary - real * q) / denominator);
}
}
/** {@inheritDoc} */
@Override
public void setSubMatrix(final double[][] subMatrix, final int row, final int column)
throws NoDataException, OutOfRangeException, DimensionMismatchException,
NullArgumentException {
if (data == null) {
if (row > 0) {
throw new MathIllegalStateException(LocalizedFormats.FIRST_ROWS_NOT_INITIALIZED_YET, row);
}
if (column > 0) {
throw new MathIllegalStateException(
LocalizedFormats.FIRST_COLUMNS_NOT_INITIALIZED_YET, column);
}
MathUtils.checkNotNull(subMatrix);
final int nRows = subMatrix.length;
if (nRows == 0) {
throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_ROW);
}
final int nCols = subMatrix[0].length;
if (nCols == 0) {
throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_COLUMN);
}
data = new double[subMatrix.length][nCols];
for (int i = 0; i < data.length; ++i) {
if (subMatrix[i].length != nCols) {
throw new DimensionMismatchException(subMatrix[i].length, nCols);
}
System.arraycopy(subMatrix[i], 0, data[i + row], column, nCols);
}
} else {
super.setSubMatrix(subMatrix, row, column);
}
}
/**
* Returns an estimate of the solution to the linear system A · x = b.
*
* @param a the linear operator A of the system
* @param b the right-hand side vector
* @return a new vector containing the solution
* @throws NullArgumentException if one of the parameters is {@code null}
* @throws NonSquareOperatorException if {@code a} is not square
* @throws DimensionMismatchException if {@code b} has dimensions inconsistent with {@code a}
* @throws MaxCountExceededException at exhaustion of the iteration count, unless a custom {@link
* org.apache.commons.math3.util.Incrementor.MaxCountExceededCallback callback} has been set
* at construction of the {@link IterationManager}
*/
public RealVector solve(final RealLinearOperator a, final RealVector b)
throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException,
MaxCountExceededException {
MathUtils.checkNotNull(a);
final RealVector x = new ArrayRealVector(a.getColumnDimension());
x.set(0.);
return solveInPlace(a, b, x);
}
/**
* Returns a {@code Complex} whose value is {@code (this - subtrahend)}. Uses the definitional
* formula
*
* <pre>
* <code>
* (a + bi) - (c + di) = (a-c) + (b-d)i
* </code>
* </pre>
*
* If either {@code this} or {@code subtrahend} has a {@code NaN]} value in either part, {@link
* #NaN} is returned; otherwise infinite and {@code NaN} values are returned in the parts of the
* result according to the rules for {@link java.lang.Double} arithmetic.
*
* @param subtrahend value to be subtracted from this {@code Complex}.
* @return {@code this - subtrahend}.
* @throws NullArgumentException if {@code subtrahend} is {@code null}.
*/
public Complex subtract(Complex subtrahend) throws NullArgumentException {
MathUtils.checkNotNull(subtrahend);
if (isNaN || subtrahend.isNaN) {
return NaN;
}
return createComplex(real - subtrahend.getReal(), imaginary - subtrahend.getImaginary());
}
/**
* Returns a {@code Complex} whose value is {@code (this + addend)}. Uses the definitional formula
*
* <pre>
* <code>
* (a + bi) + (c + di) = (a+c) + (b+d)i
* </code>
* </pre>
*
* <br>
* If either {@code this} or {@code addend} has a {@code NaN} value in either part, {@link #NaN}
* is returned; otherwise {@code Infinite} and {@code NaN} values are returned in the parts of the
* result according to the rules for {@link java.lang.Double} arithmetic.
*
* @param addend Value to be added to this {@code Complex}.
* @return {@code this + addend}.
* @throws NullArgumentException if {@code addend} is {@code null}.
*/
public Complex add(Complex addend) throws NullArgumentException {
MathUtils.checkNotNull(addend);
if (isNaN || addend.isNaN) {
return NaN;
}
return createComplex(real + addend.getReal(), imaginary + addend.getImaginary());
}
/**
* Compute mean state from osculating state.
*
* <p>Compute in a DSST sense the mean state corresponding to the input osculating state.
*
* <p>The computing is done through a fixed-point iteration process.
*
* @param osculating initial osculating state
* @return mean state
* @throws OrekitException if the underlying computation of short periodic variation fails
*/
private Orbit computeMeanOrbit(final SpacecraftState osculating) throws OrekitException {
// rough initialization of the mean parameters
EquinoctialOrbit meanOrbit = new EquinoctialOrbit(osculating.getOrbit());
// threshold for each parameter
final double epsilon = 1.0e-13;
final double thresholdA = epsilon * (1 + FastMath.abs(meanOrbit.getA()));
final double thresholdE = epsilon * (1 + meanOrbit.getE());
final double thresholdAngles = epsilon * FastMath.PI;
int i = 0;
while (i++ < 200) {
final SpacecraftState meanState =
new SpacecraftState(meanOrbit, osculating.getAttitude(), osculating.getMass());
// recompute the osculating parameters from the current mean parameters
final EquinoctialOrbit rebuilt = (EquinoctialOrbit) computeOsculatingOrbit(meanState);
// adapted parameters residuals
final double deltaA = osculating.getA() - rebuilt.getA();
final double deltaEx = osculating.getEquinoctialEx() - rebuilt.getEquinoctialEx();
final double deltaEy = osculating.getEquinoctialEy() - rebuilt.getEquinoctialEy();
final double deltaHx = osculating.getHx() - rebuilt.getHx();
final double deltaHy = osculating.getHy() - rebuilt.getHy();
final double deltaLm = MathUtils.normalizeAngle(osculating.getLM() - rebuilt.getLM(), 0.0);
// check convergence
if ((FastMath.abs(deltaA) < thresholdA)
&& (FastMath.abs(deltaEx) < thresholdE)
&& (FastMath.abs(deltaEy) < thresholdE)
&& (FastMath.abs(deltaLm) < thresholdAngles)) {
return meanOrbit;
}
// update mean parameters
meanOrbit =
new EquinoctialOrbit(
meanOrbit.getA() + deltaA,
meanOrbit.getEquinoctialEx() + deltaEx,
meanOrbit.getEquinoctialEy() + deltaEy,
meanOrbit.getHx() + deltaHx,
meanOrbit.getHy() + deltaHy,
meanOrbit.getLM() + deltaLm,
PositionAngle.MEAN,
meanOrbit.getFrame(),
meanOrbit.getDate(),
meanOrbit.getMu());
}
throw new PropagationException(OrekitMessages.UNABLE_TO_COMPUTE_DSST_MEAN_PARAMETERS, i);
}
/**
* Computes a hashcode for the matrix.
*
* @return hashcode for matrix
*/
@Override
public int hashCode() {
int ret = 7;
final int nRows = getRowDimension();
final int nCols = getColumnDimension();
ret = ret * 31 + nRows;
ret = ret * 31 + nCols;
for (int row = 0; row < nRows; ++row) {
for (int col = 0; col < nCols; ++col) {
ret = ret * 31 + (11 * (row + 1) + 17 * (col + 1)) * MathUtils.hash(getEntry(row, col));
}
}
return ret;
}
/**
* Returns a {@code Complex} whose value is {@code this * factor}. Implements preliminary checks
* for {@code NaN} and infinity followed by the definitional formula:
*
* <pre>
* <code>
* (a + bi)(c + di) = (ac - bd) + (ad + bc)i
* </code>
* </pre>
*
* Returns {@link #NaN} if either {@code this} or {@code factor} has one or more {@code NaN}
* parts. <br>
* Returns {@link #INF} if neither {@code this} nor {@code factor} has one or more {@code NaN}
* parts and if either {@code this} or {@code factor} has one or more infinite parts (same result
* is returned regardless of the sign of the components). <br>
* Returns finite values in components of the result per the definitional formula in all remaining
* cases.
*
* @param factor value to be multiplied by this {@code Complex}.
* @return {@code this * factor}.
* @throws NullArgumentException if {@code factor} is {@code null}.
*/
public Complex multiply(Complex factor) throws NullArgumentException {
MathUtils.checkNotNull(factor);
if (isNaN || factor.isNaN) {
return NaN;
}
if (Double.isInfinite(real)
|| Double.isInfinite(imaginary)
|| Double.isInfinite(factor.real)
|| Double.isInfinite(factor.imaginary)) {
// we don't use isInfinite() to avoid testing for NaN again
return INF;
}
return createComplex(
real * factor.real - imaginary * factor.imaginary,
real * factor.imaginary + imaginary * factor.real);
}
private void checkCartesianToEllipsoidic(
double ae,
double f,
double x,
double y,
double z,
double longitude,
double latitude,
double altitude)
throws OrekitException {
AbsoluteDate date = AbsoluteDate.J2000_EPOCH;
Frame frame = FramesFactory.getITRF(IERSConventions.IERS_2010, true);
OneAxisEllipsoid model = new OneAxisEllipsoid(ae, f, frame);
GeodeticPoint gp = model.transform(new Vector3D(x, y, z), frame, date);
Assert.assertEquals(longitude, MathUtils.normalizeAngle(gp.getLongitude(), longitude), 1.0e-10);
Assert.assertEquals(latitude, gp.getLatitude(), 1.0e-10);
Assert.assertEquals(altitude, gp.getAltitude(), 1.0e-10 * FastMath.abs(ae));
Vector3D rebuiltNadir = Vector3D.crossProduct(gp.getSouth(), gp.getWest());
Assert.assertEquals(0, rebuiltNadir.subtract(gp.getNadir()).getNorm(), 1.0e-15);
}
/**
* Create a new {@code FieldMatrix<T>} using the input array as the underlying data array.
*
* <p>If an array is built specially in order to be embedded in a {@code FieldMatrix<T>} and not
* used directly, the {@code copyArray} may be set to {@code false}. This will prevent the copying
* and improve performance as no new array will be built and no data will be copied.
*
* @param field Field to which the elements belong.
* @param d Data for the new matrix.
* @param copyArray Whether to copy or reference the input array.
* @throws DimensionMismatchException if {@code d} is not rectangular.
* @throws NoDataException if there are not at least one row and one column.
* @throws NullArgumentException if {@code d} is {@code null}.
* @see #Array2DRowFieldMatrix(FieldElement[][])
*/
public Array2DRowFieldMatrix(final Field<T> field, final T[][] d, final boolean copyArray)
throws DimensionMismatchException, NoDataException, NullArgumentException {
super(field);
if (copyArray) {
copyIn(d);
} else {
MathUtils.checkNotNull(d);
final int nRows = d.length;
if (nRows == 0) {
throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_ROW);
}
final int nCols = d[0].length;
if (nCols == 0) {
throw new NoDataException(LocalizedFormats.AT_LEAST_ONE_COLUMN);
}
for (int r = 1; r < nRows; r++) {
if (d[r].length != nCols) {
throw new DimensionMismatchException(nCols, d[r].length);
}
}
data = d;
}
}
/**
* Check that all elements of an array are finite real numbers.
*
* @param values Values array.
* @throws org.apache.commons.math3.exception.NotFiniteNumberException if one of the values is not
* a finite real number.
*/
private static void checkAllFiniteReal(final double[] values) {
for (int i = 0; i < values.length; i++) {
MathUtils.checkFinite(values[i]);
}
}
/**
* Returns an estimate of the solution to the linear system A · x = b.
*
* @param a the linear operator A of the system
* @param b the right-hand side vector
* @param x0 the initial guess of the solution
* @return a new vector containing the solution
* @throws NullArgumentException if one of the parameters is {@code null}
* @throws NonSquareOperatorException if {@code a} is not square
* @throws DimensionMismatchException if {@code b} or {@code x0} have dimensions inconsistent with
* {@code a}
* @throws MaxCountExceededException at exhaustion of the iteration count, unless a custom {@link
* org.apache.commons.math3.util.Incrementor.MaxCountExceededCallback callback} has been set
* at construction of the {@link IterationManager}
*/
public RealVector solve(RealLinearOperator a, RealVector b, RealVector x0)
throws NullArgumentException, NonSquareOperatorException, DimensionMismatchException,
MaxCountExceededException {
MathUtils.checkNotNull(x0);
return solveInPlace(a, b, x0.copy());
}
/**
* Returns of value of this complex number raised to the power of {@code x}. Implements the
* formula:
*
* <pre>
* <code>
* y<sup>x</sup> = exp(x·log(y))
* </code>
* </pre>
*
* where {@code exp} and {@code log} are {@link #exp} and {@link #log}, respectively. <br>
* Returns {@link Complex#NaN} if either real or imaginary part of the input argument is {@code
* NaN} or infinite, or if {@code y} equals {@link Complex#ZERO}.
*
* @param x exponent to which this {@code Complex} is to be raised.
* @return <code> this<sup>{@code x}</sup></code>.
* @throws NullArgumentException if x is {@code null}.
* @since 1.2
*/
public Complex pow(Complex x) throws NullArgumentException {
MathUtils.checkNotNull(x);
return this.log().multiply(x).exp();
}
/**
* Creates a new instance of this class, with custom iteration manager.
*
* @param manager the custom iteration manager
* @throws NullArgumentException if {@code manager} is {@code null}
*/
public IterativeLinearSolver(final IterationManager manager) throws NullArgumentException {
MathUtils.checkNotNull(manager);
this.manager = manager;
}
