Examples of org.apache.commons.math3.ode.MultistepIntegrator

org.apache.commons.math3.exception.util.ExceptionContext
This class is the base class for multistep integrators for Ordinary Differential Equations.
We define scaled derivatives s_i(n) at step n as:
```
 s₁(n) = h y'_n for first derivative s₂(n) = h²/2 y''_n for second derivative s₃(n) = h³/6 y'''_n for third derivative ... s_k(n) = h^k/k! y^(k)_n for k^th derivative 
```
Rather than storing several previous steps separately, this implementation uses the Nordsieck vector with higher degrees scaled derivatives all taken at the same step (y_n, s₁(n) and r_n) where r_n is defined as:
```
 r_n = [ s₂(n), s₃(n) ... s_k(n) ]^T 
```
(we omit the k index in the notation for clarity)

Multistep integrators with Nordsieck representation are highly sensitive to large step changes because when the step is multiplied by factor a, the k^th component of the Nordsieck vector is multiplied by a^k and the last components are the least accurate ones. The default max growth factor is therefore set to a quite low value: 2^1/order.
@see org.apache.commons.math3.ode.nonstiff.AdamsBashforthIntegrator @see org.apache.commons.math3.ode.nonstiff.AdamsMoultonIntegrator @since 2.0

                          double abs,
                          ConvergenceChecker<UnivariatePointValuePair> checker) {
        super(checker);


        if (rel < MIN_RELATIVE_TOLERANCE) {
            throw new NumberIsTooSmallException(rel, MIN_RELATIVE_TOLERANCE, true);
        }
        if (abs <= 0) {
            throw new NotStrictlyPositiveException(abs);
        }

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    @Override
    public double inverseCumulativeProbability(double p) throws OutOfRangeException {
        double ret;


        if (p < 0.0 || p > 1.0) {
            throw new OutOfRangeException(p, 0.0, 1.0);
        } else if (p == 1.0) {
            ret = Double.POSITIVE_INFINITY;
        } else {
            ret = -mean * FastMath.log(1.0 - p);
        }

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        if (lo >= hi) {
            throw new NumberIsTooLargeException(lo, hi, false);
        }
        if (init < lo ||
            init > hi) {
            throw new OutOfRangeException(init, lo, hi);
        }


        lower = lo;
        upper = hi;
        start = init;

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    @Override
    public double inverseCumulativeProbability(double p)
        throws OutOfRangeException {
        if (p < 0 || p > 1) {
            throw new OutOfRangeException(p, 0, 1);
        }
        if (p == 0) {
            return a;
        }
        if (p == 1) {

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        /**
         * {@inheritDoc}
         * @throws TooManyEvaluationsException.
         */
        public void trigger(int max) {
            throw new TooManyEvaluationsException(max);
        }

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    protected void incrementEvaluationCount()
        throws TooManyEvaluationsException {
        try {
            evaluations.incrementCount();
        } catch (MaxCountExceededException e) {
            throw new TooManyEvaluationsException(e.getMax());
        }
    }

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        /**
         * {@inheritDoc}
         * @throws TooManyIterationsException.
         */
        public void trigger(int max) {
            throw new TooManyIterationsException(max);
        }

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                                              double threshold) {
        super(wrong, threshold, false);
        this.index = index;
        this.threshold = threshold;


        final ExceptionContext context = getContext();
        context.addMessage(LocalizedFormats.NOT_POSITIVE_DEFINITE_MATRIX);
        context.addMessage(LocalizedFormats.ARRAY_ELEMENT, wrong, index);
    }

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            final double t = x.dotProduct(z);
            final double epsa = (s + MACH_PREC) * CBRT_MACH_PREC;
            if (FastMath.abs(s - t) > epsa) {
                final NonSelfAdjointOperatorException e;
                e = new NonSelfAdjointOperatorException();
                final ExceptionContext context = e.getContext();
                context.setValue(SymmLQ.OPERATOR, l);
                context.setValue(SymmLQ.VECTOR1, x);
                context.setValue(SymmLQ.VECTOR2, y);
                context.setValue(SymmLQ.THRESHOLD, Double.valueOf(epsa));
                throw e;
            }
        }

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         */
        private static void throwNPDLOException(final RealLinearOperator l,
            final RealVector v) throws NonPositiveDefiniteOperatorException {
            final NonPositiveDefiniteOperatorException e;
            e = new NonPositiveDefiniteOperatorException();
            final ExceptionContext context = e.getContext();
            context.setValue(OPERATOR, l);
            context.setValue(VECTOR, v);
            throw e;
        }

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Related Classes of org.apache.commons.math3.ode.MultistepIntegrator

org.apache.commons.math3.analysis.differentiation.DerivativeStructure

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

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

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

org.apache.commons.math3.analysis.function.Sinc

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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