Examples of org.apache.commons.math3.ode.nonstiff.EulerIntegrator

Package org.apache.commons.math3.ode.nonstiff

Examples of org.apache.commons.math3.ode.nonstiff.EulerIntegrator

org.apache.commons.math3.exception.MathIllegalArgumentException
This class implements a simple Euler integrator for Ordinary Differential Equations.
The Euler algorithm is the simplest one that can be used to integrate ordinary differential equations. It is a simple inversion of the forward difference expression : f'=(f(t+h)-f(t))/h which leads to f(t+h)=f(t)+hf'. The interpolation scheme used for dense output is the linear scheme already used for integration.

This algorithm looks cheap because it needs only one function evaluation per step. However, as it uses linear estimates, it needs very small steps to achieve high accuracy, and small steps lead to numerical errors and instabilities.

This algorithm is almost never used and has been included in this package only as a comparison reference for more useful integrators.
@see MidpointIntegrator @see ClassicalRungeKuttaIntegrator @see GillIntegrator @see ThreeEighthesIntegrator @see LutherIntegrator @since 1.2

     */
    public double correlation(final double[] xArray, final double[] yArray)
            throws DimensionMismatchException {


        if (xArray.length != yArray.length) {
            throw new DimensionMismatchException(xArray.length, yArray.length);
        }


        final int n = xArray.length;
        final long numPairs = sum(n - 1);

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     * @throws DimensionMismatchException if {@link #target} and
     * {@link #weightMatrix} have inconsistent dimensions.
     */
    private void checkParameters() {
        if (target.length != weightMatrix.getColumnDimension()) {
            throw new DimensionMismatchException(target.length,
                                                 weightMatrix.getColumnDimension());
        }
    }

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    public void increment(final double[] data)
        throws DimensionMismatchException {


        int length = data.length;
        if (length != dimension) {
            throw new DimensionMismatchException(length, dimension);
        }


        // only update the upper triangular part of the covariance matrix
        // as only these parts are actually stored
        for (int i = 0; i < length; i++){

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     * @throws DimensionMismatchException if the dimension of sc does not match this
     * @since 3.3
     */
    public void append(StorelessCovariance sc) throws DimensionMismatchException {
        if (sc.dimension != dimension) {
            throw new DimensionMismatchException(sc.dimension, dimension);
        }


        // only update the upper triangular part of the covariance matrix
        // as only these parts are actually stored
        for (int i = 0; i < dimension; i++) {

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            if (m.getColumnDimension() != m.getRowDimension()) {
                throw new NonSquareOperatorException(m.getColumnDimension(),
                                                     m.getRowDimension());
            }
            if (m.getRowDimension() != a.getRowDimension()) {
                throw new DimensionMismatchException(m.getRowDimension(),
                                                     a.getRowDimension());
            }
        }
    }

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     * length.
     */
    protected double[] computeResiduals(double[] objectiveValue) {
        final double[] target = getTarget();
        if (objectiveValue.length != target.length) {
            throw new DimensionMismatchException(target.length,
                                                 objectiveValue.length);
        }


        final double[] residuals = new double[target.length];
        for (int i = 0; i < target.length; i++) {

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   */
  public Rotation(Vector3D u, Vector3D v) throws MathArithmeticException {


    double normProduct = u.getNorm() * v.getNorm();
    if (normProduct == 0) {
        throw new MathArithmeticException(LocalizedFormats.ZERO_NORM_FOR_ROTATION_DEFINING_VECTOR);
    }


    double dot = u.dotProduct(v);


    if (dot < ((2.0e-15 - 1.0) * normProduct)) {

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     * @return the smallest prime greater than or equal to n.
     * @throws MathIllegalArgumentException if n &lt; 0.
     */
    public static int nextPrime(int n) {
        if (n < 0) {
            throw new MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL, n, 0);
        }
        if (n == 2) {
            return 2;
        }
        n |= 1;//make sure n is odd

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     * @throws MathIllegalArgumentException if n &lt; 2.
     */
    public static List<Integer> primeFactors(int n) {


        if (n < 2) {
            throw new MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL, n, 2);
        }
        // slower than trial div unless we do an awful lot of computation
        // (then it finally gets JIT-compiled efficiently
        // List<Integer> out = PollardRho.primeFactors(n);
        return SmallPrimes.trialDivision(n);

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   */
  public Rotation(Vector3D axis, double angle) throws MathIllegalArgumentException {


    double norm = axis.getNorm();
    if (norm == 0) {
      throw new MathIllegalArgumentException(LocalizedFormats.ZERO_NORM_FOR_ROTATION_AXIS);
    }


    double halfAngle = -0.5 * angle;
    double coeff = FastMath.sin(halfAngle) / norm;

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org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction

org.apache.commons.math3.analysis.function.HarmonicOscillator

org.apache.commons.math3.analysis.function.Sin

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org.apache.commons.math3.analysis.MultivariateFunction

org.apache.commons.math3.analysis.QuinticFunction

org.apache.commons.math3.analysis.solvers.BrentSolver

org.apache.commons.math3.analysis.UnivariateFunction

org.apache.commons.math3.complex.Complex

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