/*
    * 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.math4.legacy.ode.nonstiff;
  
  import org.apache.commons.math4.legacy.core.Field;
  import org.apache.commons.math4.legacy.core.RealFieldElement;
  import org.apache.commons.math4.legacy.ode.FieldEquationsMapper;
  import org.apache.commons.math4.legacy.ode.FieldODEStateAndDerivative;
  import org.apache.commons.math4.legacy.core.MathArrays;
  
  
  /**
   * This class implements the 5(4) Higham and Hall integrator for
   * Ordinary Differential Equations.
   *
   * <p>This integrator is an embedded Runge-Kutta integrator
   * of order 5(4) used in local extrapolation mode (i.e. the solution
   * is computed using the high order formula) with stepsize control
   * (and automatic step initialization) and continuous output. This
   * method uses 7 functions evaluations per step.</p>
   *
   * @param <T> the type of the field elements
   * @since 3.6
   */
  
  public class HighamHall54FieldIntegrator<T extends RealFieldElement<T>>
      extends EmbeddedRungeKuttaFieldIntegrator<T> {
  
      /** Integrator method name. */
      private static final String METHOD_NAME = "Higham-Hall 5(4)";
  
      /** Error weights Butcher array. */
      private final T[] e ;
  
      /** Simple constructor.
       * Build a fifth order Higham and Hall integrator with the given step bounds
       * @param field field to which the time and state vector elements belong
       * @param minStep minimal step (sign is irrelevant, regardless of
       * integration direction, forward or backward), the last step can
       * be smaller than this
       * @param maxStep maximal step (sign is irrelevant, regardless of
       * integration direction, forward or backward), the last step can
       * be smaller than this
       * @param scalAbsoluteTolerance allowed absolute error
       * @param scalRelativeTolerance allowed relative error
       */
      public HighamHall54FieldIntegrator(final Field<T> field,
                                         final double minStep, final double maxStep,
                                         final double scalAbsoluteTolerance,
                                         final double scalRelativeTolerance) {
          super(field, METHOD_NAME, -1,
                minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
          e = MathArrays.buildArray(field, 7);
          e[0] = fraction(-1,  20);
          e[1] = field.getZero();
          e[2] = fraction(81, 160);
          e[3] = fraction(-6,   5);
          e[4] = fraction(25,  32);
          e[5] = fraction( 1,  16);
          e[6] = fraction(-1,  10);
      }
  
      /** Simple constructor.
       * Build a fifth order Higham and Hall integrator with the given step bounds
       * @param field field to which the time and state vector elements belong
       * @param minStep minimal step (sign is irrelevant, regardless of
       * integration direction, forward or backward), the last step can
       * be smaller than this
       * @param maxStep maximal step (sign is irrelevant, regardless of
       * integration direction, forward or backward), the last step can
       * be smaller than this
       * @param vecAbsoluteTolerance allowed absolute error
       * @param vecRelativeTolerance allowed relative error
       */
      public HighamHall54FieldIntegrator(final Field<T> field,
                                         final double minStep, final double maxStep,
                                         final double[] vecAbsoluteTolerance,
                                         final double[] vecRelativeTolerance) {
          super(field, METHOD_NAME, -1,
                minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
          e = MathArrays.buildArray(field, 7);
          e[0] = fraction(-1,  20);
          e[1] = field.getZero();
          e[2] = fraction(81, 160);
         e[3] = fraction(-6,   5);
         e[4] = fraction(25,  32);
         e[5] = fraction( 1,  16);
         e[6] = fraction(-1,  10);
     }
 
     /** {@inheritDoc} */
     @Override
     public T[] getC() {
         final T[] c = MathArrays.buildArray(getField(), 6);
         c[0] = fraction(2, 9);
         c[1] = fraction(1, 3);
         c[2] = fraction(1, 2);
         c[3] = fraction(3, 5);
         c[4] = getField().getOne();
         c[5] = getField().getOne();
         return c;
     }
 
     /** {@inheritDoc} */
     @Override
     public T[][] getA() {
         final T[][] a = MathArrays.buildArray(getField(), 6, -1);
         for (int i = 0; i < a.length; ++i) {
             a[i] = MathArrays.buildArray(getField(), i + 1);
         }
         a[0][0] = fraction(     2,     9);
         a[1][0] = fraction(     1,    12);
         a[1][1] = fraction(     1,     4);
         a[2][0] = fraction(     1,     8);
         a[2][1] = getField().getZero();
         a[2][2] = fraction(     3,     8);
         a[3][0] = fraction(    91,   500);
         a[3][1] = fraction(   -27,   100);
         a[3][2] = fraction(    78,   125);
         a[3][3] = fraction(     8,   125);
         a[4][0] = fraction(   -11,    20);
         a[4][1] = fraction(    27,    20);
         a[4][2] = fraction(    12,     5);
         a[4][3] = fraction(   -36,     5);
         a[4][4] = fraction(     5,     1);
         a[5][0] = fraction(     1,    12);
         a[5][1] = getField().getZero();
         a[5][2] = fraction(    27,    32);
         a[5][3] = fraction(    -4,     3);
         a[5][4] = fraction(   125,    96);
         a[5][5] = fraction(     5,    48);
         return a;
     }
 
     /** {@inheritDoc} */
     @Override
     public T[] getB() {
         final T[] b = MathArrays.buildArray(getField(), 7);
         b[0] = fraction(  1, 12);
         b[1] = getField().getZero();
         b[2] = fraction( 27, 32);
         b[3] = fraction( -4,  3);
         b[4] = fraction(125, 96);
         b[5] = fraction(  5, 48);
         b[6] = getField().getZero();
         return b;
     }
 
     /** {@inheritDoc} */
     @Override
     protected HighamHall54FieldStepInterpolator<T>
         createInterpolator(final boolean forward, T[][] yDotK,
                            final FieldODEStateAndDerivative<T> globalPreviousState,
                            final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper<T> mapper) {
         return new HighamHall54FieldStepInterpolator<>(getField(), forward, yDotK,
                                                         globalPreviousState, globalCurrentState,
                                                         globalPreviousState, globalCurrentState,
                                                         mapper);
     }
 
     /** {@inheritDoc} */
     @Override
     public int getOrder() {
         return 5;
     }
 
     /** {@inheritDoc} */
     @Override
     protected T estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) {
 
         T error = getField().getZero();
 
         for (int j = 0; j < mainSetDimension; ++j) {
             T errSum = yDotK[0][j].multiply(e[0]);
             for (int l = 1; l < e.length; ++l) {
                 errSum = errSum.add(yDotK[l][j].multiply(e[l]));
             }
 
             final T yScale = RealFieldElement.max(y0[j].abs(), y1[j].abs());
             final T tol    = (vecAbsoluteTolerance == null) ?
                              yScale.multiply(scalRelativeTolerance).add(scalAbsoluteTolerance) :
                              yScale.multiply(vecRelativeTolerance[j]).add(vecAbsoluteTolerance[j]);
             final T ratio  = h.multiply(errSum).divide(tol);
             error = error.add(ratio.multiply(ratio));
         }
 
         return error.divide(mainSetDimension).sqrt();
     }
 }