001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    package org.apache.commons.nabla.numerical;
018    
019    import org.apache.commons.nabla.core.DifferentialPair;
020    import org.apache.commons.nabla.core.UnivariateDerivative;
021    import org.apache.commons.nabla.core.UnivariateDifferentiable;
022    
023    /** Four-points finite differences scheme.
024     * The error model for the four-points scheme is
025     * <code>-2h<sup>4</sup>/5 f<sup>(5)</sup>(x) + O(h<sup>6</sup>)</code>.
026     */
027    public class FourPointsScheme extends FiniteDifferencesDifferentiator {
028    
029        /** Serializable UID. */
030        private static final long serialVersionUID = 3216911780962952859L;
031    
032        /** Scheme denominator. */
033        private final double denominator;
034    
035        /** Build a 4-points finite differences scheme.
036         * @param h differences step size
037         */
038        public FourPointsScheme(final double h) {
039            super(h, -2 * h * h * h * h / 5, 5);
040            denominator = 12 * h;
041        }
042    
043        /** {@inheritDoc} */
044        public UnivariateDerivative differentiate(final UnivariateDifferentiable d) {
045            return new UnivariateDerivative() {
046    
047                /** {@inheritDoc} */
048                public UnivariateDifferentiable getPrimitive() {
049                    return d;
050                }
051    
052                /** {@inheritDoc} */
053                public DifferentialPair f(final DifferentialPair t) {
054                    final double h = getStepSize();
055                    final double u0 = t.getValue();
056                    final double ft = d.f(u0);
057                    final double d1 = d.f(u0 +     h) - d.f(u0 -     h);
058                    final double d2 = d.f(u0 + 2 * h) - d.f(u0 - 2 * h);
059                    return new DifferentialPair(ft, t.getFirstDerivative() * (8 * d1 - d2) / denominator);
060                }
061    
062            };
063        }
064    
065    }