RcRealDuplication.java

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 * this work for additional information regarding copyright ownership.
 * The Hipparchus project licenses this file to You under the Apache License, Version 2.0
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 *      https://www.apache.org/licenses/LICENSE-2.0
 *
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 * distributed under the License is distributed on an "AS IS" BASIS,
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 * See the License for the specific language governing permissions and
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package org.hipparchus.special.elliptic.carlson;

import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;

/** Duplication algorithm for Carlson R<sub>C</sub> elliptic integral.
 * @since 2.0
 */
class RcRealDuplication extends RealDuplication {

    /** Constant term in R<sub>C</sub> polynomial. */
    static final double S0 = 80080;

    /** Coefficient of s² in R<sub>C</sub> polynomial. */
    static final double S2 = 24024;

    /** Coefficient of s³ in R<sub>C</sub> polynomial. */
    static final double S3 = 11440;

    /** Coefficient of s⁴ in R<sub>C</sub> polynomial. */
    static final double S4 = 30030;

    /** Coefficient of s⁵ in R<sub>C</sub> polynomial. */
    static final double S5 = 32760;

    /** Coefficient of s⁶ in R<sub>C</sub> polynomial. */
    static final double S6 = 61215;

    /** Coefficient of s⁷ in R<sub>C</sub> polynomial. */
    static final double S7 = 90090;

    /** Denominator in R<sub>C</sub> polynomial. */
    static final double DENOMINATOR = 80080;

    /** Simple constructor.
     * @param x first symmetric variable of the integral
     * @param y second symmetric variable of the integral
     */
    RcRealDuplication(final double x, final double y) {
        super(x, y);
    }

    /** {@inheritDoc} */
    @Override
    protected void initialMeanPoint(final double[] va) {
        va[2] =  (va[0] + va[1] * 2) / 3.0;
    }

    /** {@inheritDoc} */
    @Override
    protected double convergenceCriterion(final double r, final double max) {
        return max / FastMath.sqrt(FastMath.sqrt(FastMath.sqrt(r * 3.0)));
    }

    /** {@inheritDoc} */
    @Override
    protected void update(final int m, final double[] vaM, final double[] sqrtM, final  double fourM) {
        final double lambdaA = sqrtM[0] * sqrtM[1] * 2;
        final double lambdaB = vaM[1];
        vaM[0] = MathArrays.linearCombination(0.25, vaM[0], 0.25, lambdaA, 0.25, lambdaB); // xₘ
        vaM[1] = MathArrays.linearCombination(0.25, vaM[1], 0.25, lambdaA, 0.25, lambdaB); // yₘ
        vaM[2] = MathArrays.linearCombination(0.25, vaM[2], 0.25, lambdaA, 0.25, lambdaB); // aₘ
    }

    /** {@inheritDoc} */
    @Override
    protected double evaluate(final double[] va0, final double aM, final  double fourM) {

        // compute the single polynomial independent variable
        final double s = (va0[1] - va0[2]) / (aM * fourM);

        // evaluate integral using equation 2.13 in Carlson[1995]
        final double poly = ((((((S7 * s + S6) * s + S5) * s + S4) * s + S3) * s + S2) * s * s + S0) / DENOMINATOR;
        return poly / FastMath.sqrt(aM);

    }

}