/*

  * Licensed to the Apache Software Foundation (ASF) under one or more

  * contributor license agreements.  See the NOTICE file distributed with

  * this work for additional information regarding copyright ownership.

  * The ASF licenses this file to You 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 org.apache.commons.nabla.differences;

 import org.apache.commons.nabla.core.DifferentialPair;

 import org.apache.commons.nabla.core.UnivariateDerivative;

 import org.apache.commons.nabla.core.UnivariateDifferentiable;

 /** Eight-points finite differences scheme.

  * The error model for the eight-points scheme is

  * <code>-h<sup>8</sup>/630 f<sup>(9)</sup>(x) + O(h<sup>10</sup>)</code>.

  */

 public class EightPointsScheme extends FiniteDifferencesDifferentiator {

     /** Serializable UID. */

     private static final long serialVersionUID = 3498050520014763473L;

     /** Scheme denominator. */

     private final double denominator;

     /** Build an 8-points finite differences scheme.

      * @param h differences step size

      */

     public EightPointsScheme(final double h) {

         super(h, -h * h * h * h * h * h * h * h / 630, 9);

         denominator = 840 * h;

     }

     /** {@inheritDoc} */

     public UnivariateDerivative differentiate(final UnivariateDifferentiable d) {

         return new UnivariateDerivative() {

             public UnivariateDifferentiable getPrimitive() {

                 return d;

             }

             public DifferentialPair f(final DifferentialPair t) {

                 final double h = getStepSize();

                 final double u0 = t.getValue();

                 final double ft = d.f(u0);

                 final double d1 = d.f(u0 +     h) - d.f(u0 -     h);

                 final double d2 = d.f(u0 + 2 * h) - d.f(u0 - 2 * h);

                 final double d3 = d.f(u0 + 3 * h) - d.f(u0 - 3 * h);

                 final double d4 = d.f(u0 + 4 * h) - d.f(u0 - 4 * h);

                 return new DifferentialPair(ft, t.getFirstDerivative() * (-3 * d4 + 32 * d3 - 168 * d2 + 672 * d1) / denominator);

             }

         };

     }

 }