SymmetricDerivativeEstimator.java

/*
 * Copyright (C) 2012 Alberto Irurueta Carro (alberto@irurueta.com)
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *         http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package com.irurueta.numerical;

/**
 * Class to estimate the derivative of a single dimension function at a given
 * point.
 * The algorithm used in this implementation is valid for continuous functions
 * only, otherwise inaccurate results might be obtained.
 * This implementation is more accurate although slower than
 * DerivativeEstimator.
 */
public class SymmetricDerivativeEstimator extends DerivativeEstimator {

    /**
     * Constructor.
     *
     * @param listener listener to evaluate a single dimension function.
     */
    public SymmetricDerivativeEstimator(final SingleDimensionFunctionEvaluatorListener listener) {
        super(listener);
    }

    /**
     * Computes the function derivative at provided point x.
     *
     * @param x Point where derivative is estimated.
     * @return Derivative of function at provided point.
     * @throws EvaluationException Raised if function cannot be properly
     *                             evaluated.
     */
    @Override
    public double derivative(final double x) throws EvaluationException {
        var h = EPS * Math.abs(x);
        if (h == 0.0) {
            // Trick to reduce finite-precision error
            h = EPS;
        }

        final var xh1 = x + h;
        final var xh2 = x - h;
        // because of machine precision h could be different in both cases
        final var h1 = xh1 - x;
        final var h2 = x - xh2;

        // this is more or less equal to 2.0 * h
        final var hh = h1 + h2;

        final var fh1 = listener.evaluate(xh1);
        final var fh2 = listener.evaluate(xh2);

        return (fh1 - fh2) / hh;
    }
}