Package org.apache.commons.math3.analysis

Examples of org.apache.commons.math3.analysis.Expm1Function


     * <p>
     * |expm1^(n)(zeta)| <= e, zeta in [-1, 1]
     */
    @Test
    public void testExpm1Function() {
        UnivariateFunction f = new Expm1Function();
        UnivariateInterpolator interpolator = new NevilleInterpolator();
        double x[], y[], z, expected, result, tolerance;

        // 5 interpolating points on interval [-1, 1]
        int n = 5;
        double min = -1.0, max = 1.0;
        x = new double[n];
        y = new double[n];
        for (int i = 0; i < n; i++) {
            x[i] = min + i * (max - min) / n;
            y[i] = f.value(x[i]);
        }
        double derivativebound = FastMath.E;
        UnivariateFunction p = interpolator.interpolate(x, y);

        z = 0.0; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);

        z = 0.5; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);

        z = -0.5; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);
    }
View Full Code Here


     * <p>
     * |expm1^(n)(zeta)| <= e, zeta in [-1, 1]
     */
    @Test
    public void testExpm1Function() {
        UnivariateFunction f = new Expm1Function();
        UnivariateInterpolator interpolator = new DividedDifferenceInterpolator();
        double x[], y[], z, expected, result, tolerance;

        // 5 interpolating points on interval [-1, 1]
        int n = 5;
        double min = -1.0, max = 1.0;
        x = new double[n];
        y = new double[n];
        for (int i = 0; i < n; i++) {
            x[i] = min + i * (max - min) / n;
            y[i] = f.value(x[i]);
        }
        double derivativebound = FastMath.E;
        UnivariateFunction p = interpolator.interpolate(x, y);

        z = 0.0; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);

        z = 0.5; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);

        z = -0.5; expected = f.value(z); result = p.value(z);
        tolerance = FastMath.abs(derivativebound * partialerror(x, z));
        Assert.assertEquals(expected, result, tolerance);
    }
View Full Code Here

    /**
     * Test of solver for the exponential function.
     */
    @Test
    public void testExpm1Function() {
        UnivariateFunction f = new Expm1Function();
        UnivariateSolver solver = new RiddersSolver();
        double min, max, expected, result, tolerance;

        min = -1.0; max = 2.0; expected = 0.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
View Full Code Here

     * <p>
     * It takes 25 to 50 iterations for the last two tests to converge.
     */
    @Test
    public void testExpm1Function() {
        UnivariateFunction f = new Expm1Function();
        UnivariateSolver solver = new MullerSolver2();
        double min, max, expected, result, tolerance;

        min = -1.0; max = 2.0; expected = 0.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
View Full Code Here

     * In fact, if not for the bisection alternative, the solver would
     * exceed the default maximal iteration of 100.
     */
    @Test
    public void testExpm1Function() {
        UnivariateFunction f = new Expm1Function();
        UnivariateSolver solver = new MullerSolver();
        double min, max, expected, result, tolerance;

        min = -1.0; max = 2.0; expected = 0.0;
        tolerance = FastMath.max(solver.getAbsoluteAccuracy(),
View Full Code Here

                return false;
            }
            final int    n = FastMath.max(1, (int) FastMath.ceil(FastMath.abs(dt) / maxCheckInterval));
            final double h = dt / n;

            final UnivariateFunction f = new UnivariateFunction() {
                public double value(final double t) throws LocalMaxCountExceededException {
                    try {
                        interpolator.setInterpolatedTime(t);
                        return handler.g(t, getCompleteState(interpolator));
                    } catch (MaxCountExceededException mcee) {
                        throw new LocalMaxCountExceededException(mcee);
                    }
                }
            };

            double ta = t0;
            double ga = g0;
            for (int i = 0; i < n; ++i) {

                // evaluate handler value at the end of the substep
                final double tb = t0 + (i + 1) * h;
                interpolator.setInterpolatedTime(tb);
                final double gb = handler.g(tb, getCompleteState(interpolator));

                // check events occurrence
                if (g0Positive ^ (gb >= 0)) {
                    // there is a sign change: an event is expected during this step

                    // variation direction, with respect to the integration direction
                    increasing = gb >= ga;

                    // find the event time making sure we select a solution just at or past the exact root
                    final double root;
                    if (solver instanceof BracketedUnivariateSolver<?>) {
                        @SuppressWarnings("unchecked")
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                (BracketedUnivariateSolver<UnivariateFunction>) solver;
                        root = forward ?
                               bracketing.solve(maxIterationCount, f, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               bracketing.solve(maxIterationCount, f, tb, ta, AllowedSolution.LEFT_SIDE);
                    } else {
                        final double baseRoot = forward ?
                                                solver.solve(maxIterationCount, f, ta, tb) :
                                                solver.solve(maxIterationCount, f, tb, ta);
                        final int remainingEval = maxIterationCount - solver.getEvaluations();
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
                        root = forward ?
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);
                    }

                    if ((!Double.isNaN(previousEventTime)) &&
                        (FastMath.abs(root - ta) <= convergence) &&
                        (FastMath.abs(root - previousEventTime) <= convergence)) {
                        // we have either found nothing or found (again ?) a past event,
                        // retry the substep excluding this value, and taking care to have the
                        // required sign in case the g function is noisy around its zero and
                        // crosses the axis several times
                        do {
                            ta = forward ? ta + convergence : ta - convergence;
                            ga = f.value(ta);
                        } while ((g0Positive ^ (ga >= 0)) && (forward ^ (ta >= tb)));
                        --i;
                    } else if (Double.isNaN(previousEventTime) ||
                               (FastMath.abs(previousEventTime - root) > convergence)) {
                        pendingEventTime = root;
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                        final double baseRoot = forward ?
                                                solver.solve(maxIterationCount, f, ta, tb) :
                                                solver.solve(maxIterationCount, f, tb, ta);
                        final int remainingEval = maxIterationCount - solver.getEvaluations();
                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
                                new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
                        root = forward ?
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
                                                                   baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);
View Full Code Here

                // tests for termination and stringent tolerances
                if (FastMath.abs(actRed) <= TWO_EPS &&
                    preRed <= TWO_EPS &&
                    ratio <= 2.0) {
                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_COST_RELATIVE_TOLERANCE,
                                                   costRelativeTolerance);
                } else if (delta <= TWO_EPS * xNorm) {
                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_PARAMETERS_RELATIVE_TOLERANCE,
                                                   parRelativeTolerance);
                } else if (maxCosine <= TWO_EPS) {
                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_ORTHOGONALITY_TOLERANCE,
                                                   orthoTolerance);
                }
            }
        }
    }
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                for (int j = k; j < nR; ++j) {
                    double aki = weightedJacobian[j][permutation[i]];
                    norm2 += aki * aki;
                }
                if (Double.isInfinite(norm2) || Double.isNaN(norm2)) {
                    throw new ConvergenceException(LocalizedFormats.UNABLE_TO_PERFORM_QR_DECOMPOSITION_ON_JACOBIAN,
                                                   nR, nC);
                }
                if (norm2 > ak2) {
                    nextColumn = i;
                    ak2        = norm2;
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                }

                // tests for termination and stringent tolerances
                // (2.2204e-16 is the machine epsilon for IEEE754)
                if ((FastMath.abs(actRed) <= 2.2204e-16) && (preRed <= 2.2204e-16) && (ratio <= 2.0)) {
                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_COST_RELATIVE_TOLERANCE,
                                                   costRelativeTolerance);
                } else if (delta <= 2.2204e-16 * xNorm) {
                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_PARAMETERS_RELATIVE_TOLERANCE,
                                                   parRelativeTolerance);
                } else if (maxCosine <= 2.2204e-16)  {
                    throw new ConvergenceException(LocalizedFormats.TOO_SMALL_ORTHOGONALITY_TOLERANCE,
                                                   orthoTolerance);
                }
            }
        }
    }
View Full Code Here

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