/*
    * 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.analysis.interpolation;
  
  import org.apache.commons.math4.legacy.analysis.TrivariateFunction;
  import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
  import org.apache.commons.math4.legacy.exception.NoDataException;
  import org.apache.commons.math4.legacy.exception.NonMonotonicSequenceException;
  import org.apache.commons.math4.legacy.exception.OutOfRangeException;
  import org.apache.commons.math4.legacy.core.MathArrays;
  
  /**
   * Function that implements the
   * <a href="http://en.wikipedia.org/wiki/Tricubic_interpolation">
   * tricubic spline interpolation</a>, as proposed in
   * <blockquote>
   *  Tricubic interpolation in three dimensions<br>
   *  F. Lekien and J. Marsden<br>
   *  <em>Int. J. Numer. Meth. Eng</em> 2005; <b>63</b>:455-471<br>
   * </blockquote>
   *
   * @since 3.4.
   */
  public class TricubicInterpolatingFunction
      implements TrivariateFunction {
      /**
       * Matrix to compute the spline coefficients from the function values
       * and function derivatives values.
       */
      private static final double[][] AINV = {
          { 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { -3,3,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 2,-2,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { -3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 9,-9,-9,9,0,0,0,0,6,3,-6,-3,0,0,0,0,6,-6,3,-3,0,0,0,0,0,0,0,0,0,0,0,0,4,2,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { -6,6,6,-6,0,0,0,0,-3,-3,3,3,0,0,0,0,-4,4,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { -6,6,6,-6,0,0,0,0,-4,-2,4,2,0,0,0,0,-3,3,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 4,-4,-4,4,0,0,0,0,2,2,-2,-2,0,0,0,0,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,1,1,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-9,-9,9,0,0,0,0,0,0,0,0,0,0,0,0,6,3,-6,-3,0,0,0,0,6,-6,3,-3,0,0,0,0,4,2,2,1,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,6,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,3,3,0,0,0,0,-4,4,-2,2,0,0,0,0,-2,-2,-1,-1,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,6,6,-6,0,0,0,0,0,0,0,0,0,0,0,0,-4,-2,4,2,0,0,0,0,-3,3,-3,3,0,0,0,0,-2,-1,-2,-1,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,0,0,0,0,2,-2,2,-2,0,0,0,0,1,1,1,1,0,0,0,0 },
          {-3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,-3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 9,-9,0,0,-9,9,0,0,6,3,0,0,-6,-3,0,0,0,0,0,0,0,0,0,0,6,-6,0,0,3,-3,0,0,0,0,0,0,0,0,0,0,4,2,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { -6,6,0,0,6,-6,0,0,-3,-3,0,0,3,3,0,0,0,0,0,0,0,0,0,0,-4,4,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,-1,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-9,0,0,-9,9,0,0,0,0,0,0,0,0,0,0,6,3,0,0,-6,-3,0,0,0,0,0,0,0,0,0,0,6,-6,0,0,3,-3,0,0,4,2,0,0,2,1,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,6,0,0,6,-6,0,0,0,0,0,0,0,0,0,0,-3,-3,0,0,3,3,0,0,0,0,0,0,0,0,0,0,-4,4,0,0,-2,2,0,0,-2,-2,0,0,-1,-1,0,0 },
          { 9,0,-9,0,-9,0,9,0,0,0,0,0,0,0,0,0,6,0,3,0,-6,0,-3,0,6,0,-6,0,3,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,2,0,2,0,1,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,9,0,-9,0,-9,0,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,3,0,-6,0,-3,0,6,0,-6,0,3,0,-3,0,0,0,0,0,0,0,0,0,4,0,2,0,2,0,1,0 },
          { -27,27,27,-27,27,-27,-27,27,-18,-9,18,9,18,9,-18,-9,-18,18,-9,9,18,-18,9,-9,-18,18,18,-18,-9,9,9,-9,-12,-6,-6,-3,12,6,6,3,-12,-6,12,6,-6,-3,6,3,-12,12,-6,6,-6,6,-3,3,-8,-4,-4,-2,-4,-2,-2,-1 },
          { 18,-18,-18,18,-18,18,18,-18,9,9,-9,-9,-9,-9,9,9,12,-12,6,-6,-12,12,-6,6,12,-12,-12,12,6,-6,-6,6,6,6,3,3,-6,-6,-3,-3,6,6,-6,-6,3,3,-3,-3,8,-8,4,-4,4,-4,2,-2,4,4,2,2,2,2,1,1 },
          { -6,0,6,0,6,0,-6,0,0,0,0,0,0,0,0,0,-3,0,-3,0,3,0,3,0,-4,0,4,0,-2,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-2,0,-1,0,-1,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,-6,0,6,0,6,0,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,-3,0,3,0,3,0,-4,0,4,0,-2,0,2,0,0,0,0,0,0,0,0,0,-2,0,-2,0,-1,0,-1,0 },
          { 18,-18,-18,18,-18,18,18,-18,12,6,-12,-6,-12,-6,12,6,9,-9,9,-9,-9,9,-9,9,12,-12,-12,12,6,-6,-6,6,6,3,6,3,-6,-3,-6,-3,8,4,-8,-4,4,2,-4,-2,6,-6,6,-6,3,-3,3,-3,4,2,4,2,2,1,2,1 },
          { -12,12,12,-12,12,-12,-12,12,-6,-6,6,6,6,6,-6,-6,-6,6,-6,6,6,-6,6,-6,-8,8,8,-8,-4,4,4,-4,-3,-3,-3,-3,3,3,3,3,-4,-4,4,4,-2,-2,2,2,-4,4,-4,4,-2,2,-2,2,-2,-2,-2,-2,-1,-1,-1,-1 },
          { 2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { -6,6,0,0,6,-6,0,0,-4,-2,0,0,4,2,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,-3,3,0,0,0,0,0,0,0,0,0,0,-2,-1,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 4,-4,0,0,-4,4,0,0,2,2,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0 },
          { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-6,6,0,0,6,-6,0,0,0,0,0,0,0,0,0,0,-4,-2,0,0,4,2,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,-3,3,0,0,-2,-1,0,0,-2,-1,0,0 },
         { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,0,-4,4,0,0,0,0,0,0,0,0,0,0,2,2,0,0,-2,-2,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,2,-2,0,0,1,1,0,0,1,1,0,0 },
         { -6,0,6,0,6,0,-6,0,0,0,0,0,0,0,0,0,-4,0,-2,0,4,0,2,0,-3,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,-2,0,-1,0,0,0,0,0,0,0,0,0 },
         { 0,0,0,0,0,0,0,0,-6,0,6,0,6,0,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,-2,0,4,0,2,0,-3,0,3,0,-3,0,3,0,0,0,0,0,0,0,0,0,-2,0,-1,0,-2,0,-1,0 },
         { 18,-18,-18,18,-18,18,18,-18,12,6,-12,-6,-12,-6,12,6,12,-12,6,-6,-12,12,-6,6,9,-9,-9,9,9,-9,-9,9,8,4,4,2,-8,-4,-4,-2,6,3,-6,-3,6,3,-6,-3,6,-6,3,-3,6,-6,3,-3,4,2,2,1,4,2,2,1 },
         { -12,12,12,-12,12,-12,-12,12,-6,-6,6,6,6,6,-6,-6,-8,8,-4,4,8,-8,4,-4,-6,6,6,-6,-6,6,6,-6,-4,-4,-2,-2,4,4,2,2,-3,-3,3,3,-3,-3,3,3,-4,4,-2,2,-4,4,-2,2,-2,-2,-1,-1,-2,-2,-1,-1 },
         { 4,0,-4,0,-4,0,4,0,0,0,0,0,0,0,0,0,2,0,2,0,-2,0,-2,0,2,0,-2,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0 },
         { 0,0,0,0,0,0,0,0,4,0,-4,0,-4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,2,0,-2,0,-2,0,2,0,-2,0,2,0,-2,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0 },
         { -12,12,12,-12,12,-12,-12,12,-8,-4,8,4,8,4,-8,-4,-6,6,-6,6,6,-6,6,-6,-6,6,6,-6,-6,6,6,-6,-4,-2,-4,-2,4,2,4,2,-4,-2,4,2,-4,-2,4,2,-3,3,-3,3,-3,3,-3,3,-2,-1,-2,-1,-2,-1,-2,-1 },
         { 8,-8,-8,8,-8,8,8,-8,4,4,-4,-4,-4,-4,4,4,4,-4,4,-4,-4,4,-4,4,4,-4,-4,4,4,-4,-4,4,2,2,2,2,-2,-2,-2,-2,2,2,-2,-2,2,2,-2,-2,2,-2,2,-2,2,-2,2,-2,1,1,1,1,1,1,1,1 }
     };
 
     /** Samples x-coordinates. */
     private final double[] xval;
     /** Samples y-coordinates. */
     private final double[] yval;
     /** Samples z-coordinates. */
     private final double[] zval;
     /** Set of cubic splines patching the whole data grid. */
     private final TricubicFunction[][][] splines;
 
     /**
      * @param x Sample values of the x-coordinate, in increasing order.
      * @param y Sample values of the y-coordinate, in increasing order.
      * @param z Sample values of the y-coordinate, in increasing order.
      * @param f Values of the function on every grid point.
      * @param dFdX Values of the partial derivative of function with respect to x on every grid point.
      * @param dFdY Values of the partial derivative of function with respect to y on every grid point.
      * @param dFdZ Values of the partial derivative of function with respect to z on every grid point.
      * @param d2FdXdY Values of the cross partial derivative of function on every grid point.
      * @param d2FdXdZ Values of the cross partial derivative of function on every grid point.
      * @param d2FdYdZ Values of the cross partial derivative of function on every grid point.
      * @param d3FdXdYdZ Values of the cross partial derivative of function on every grid point.
      * @throws NoDataException if any of the arrays has zero length.
      * @throws DimensionMismatchException if the various arrays do not contain the expected number of elements.
      * @throws NonMonotonicSequenceException if {@code x}, {@code y} or {@code z} are not strictly increasing.
      */
     public TricubicInterpolatingFunction(double[] x,
                                          double[] y,
                                          double[] z,
                                          double[][][] f,
                                          double[][][] dFdX,
                                          double[][][] dFdY,
                                          double[][][] dFdZ,
                                          double[][][] d2FdXdY,
                                          double[][][] d2FdXdZ,
                                          double[][][] d2FdYdZ,
                                          double[][][] d3FdXdYdZ)
         throws NoDataException,
                DimensionMismatchException,
                NonMonotonicSequenceException {
         final int xLen = x.length;
         final int yLen = y.length;
         final int zLen = z.length;
 
         if (xLen == 0 || yLen == 0 || z.length == 0 || f.length == 0 || f[0].length == 0) {
             throw new NoDataException();
         }
         if (xLen != f.length) {
             throw new DimensionMismatchException(xLen, f.length);
         }
         if (xLen != dFdX.length) {
             throw new DimensionMismatchException(xLen, dFdX.length);
         }
         if (xLen != dFdY.length) {
             throw new DimensionMismatchException(xLen, dFdY.length);
         }
         if (xLen != dFdZ.length) {
             throw new DimensionMismatchException(xLen, dFdZ.length);
         }
         if (xLen != d2FdXdY.length) {
             throw new DimensionMismatchException(xLen, d2FdXdY.length);
         }
         if (xLen != d2FdXdZ.length) {
             throw new DimensionMismatchException(xLen, d2FdXdZ.length);
         }
         if (xLen != d2FdYdZ.length) {
             throw new DimensionMismatchException(xLen, d2FdYdZ.length);
         }
         if (xLen != d3FdXdYdZ.length) {
             throw new DimensionMismatchException(xLen, d3FdXdYdZ.length);
         }
 
         MathArrays.checkOrder(x);
         MathArrays.checkOrder(y);
         MathArrays.checkOrder(z);
 
         xval = x.clone();
         yval = y.clone();
         zval = z.clone();
 
         final int lastI = xLen - 1;
         final int lastJ = yLen - 1;
         final int lastK = zLen - 1;
         splines = new TricubicFunction[lastI][lastJ][lastK];
 
         for (int i = 0; i < lastI; i++) {
             if (f[i].length != yLen) {
                 throw new DimensionMismatchException(f[i].length, yLen);
             }
             if (dFdX[i].length != yLen) {
                 throw new DimensionMismatchException(dFdX[i].length, yLen);
             }
             if (dFdY[i].length != yLen) {
                 throw new DimensionMismatchException(dFdY[i].length, yLen);
             }
             if (dFdZ[i].length != yLen) {
                 throw new DimensionMismatchException(dFdZ[i].length, yLen);
             }
             if (d2FdXdY[i].length != yLen) {
                 throw new DimensionMismatchException(d2FdXdY[i].length, yLen);
             }
             if (d2FdXdZ[i].length != yLen) {
                 throw new DimensionMismatchException(d2FdXdZ[i].length, yLen);
             }
             if (d2FdYdZ[i].length != yLen) {
                 throw new DimensionMismatchException(d2FdYdZ[i].length, yLen);
             }
             if (d3FdXdYdZ[i].length != yLen) {
                 throw new DimensionMismatchException(d3FdXdYdZ[i].length, yLen);
             }
 
             final int ip1 = i + 1;
             final double xR = xval[ip1] - xval[i];
             for (int j = 0; j < lastJ; j++) {
                 if (f[i][j].length != zLen) {
                     throw new DimensionMismatchException(f[i][j].length, zLen);
                 }
                 if (dFdX[i][j].length != zLen) {
                     throw new DimensionMismatchException(dFdX[i][j].length, zLen);
                 }
                 if (dFdY[i][j].length != zLen) {
                     throw new DimensionMismatchException(dFdY[i][j].length, zLen);
                 }
                 if (dFdZ[i][j].length != zLen) {
                     throw new DimensionMismatchException(dFdZ[i][j].length, zLen);
                 }
                 if (d2FdXdY[i][j].length != zLen) {
                     throw new DimensionMismatchException(d2FdXdY[i][j].length, zLen);
                 }
                 if (d2FdXdZ[i][j].length != zLen) {
                     throw new DimensionMismatchException(d2FdXdZ[i][j].length, zLen);
                 }
                 if (d2FdYdZ[i][j].length != zLen) {
                     throw new DimensionMismatchException(d2FdYdZ[i][j].length, zLen);
                 }
                 if (d3FdXdYdZ[i][j].length != zLen) {
                     throw new DimensionMismatchException(d3FdXdYdZ[i][j].length, zLen);
                 }
 
                 final int jp1 = j + 1;
                 final double yR = yval[jp1] - yval[j];
                 final double xRyR = xR * yR;
                 for (int k = 0; k < lastK; k++) {
                     final int kp1 = k + 1;
                     final double zR = zval[kp1] - zval[k];
                     final double xRzR = xR * zR;
                     final double yRzR = yR * zR;
                     final double xRyRzR = xR * yRzR;
 
                     final double[] beta = new double[] {
                         f[i][j][k], f[ip1][j][k],
                         f[i][jp1][k], f[ip1][jp1][k],
                         f[i][j][kp1], f[ip1][j][kp1],
                         f[i][jp1][kp1], f[ip1][jp1][kp1],
 
                         dFdX[i][j][k] * xR, dFdX[ip1][j][k] * xR,
                         dFdX[i][jp1][k] * xR, dFdX[ip1][jp1][k] * xR,
                         dFdX[i][j][kp1] * xR, dFdX[ip1][j][kp1] * xR,
                         dFdX[i][jp1][kp1] * xR, dFdX[ip1][jp1][kp1] * xR,
 
                         dFdY[i][j][k] * yR, dFdY[ip1][j][k] * yR,
                         dFdY[i][jp1][k] * yR, dFdY[ip1][jp1][k] * yR,
                         dFdY[i][j][kp1] * yR, dFdY[ip1][j][kp1] * yR,
                         dFdY[i][jp1][kp1] * yR, dFdY[ip1][jp1][kp1] * yR,
 
                         dFdZ[i][j][k] * zR, dFdZ[ip1][j][k] * zR,
                         dFdZ[i][jp1][k] * zR, dFdZ[ip1][jp1][k] * zR,
                         dFdZ[i][j][kp1] * zR, dFdZ[ip1][j][kp1] * zR,
                         dFdZ[i][jp1][kp1] * zR, dFdZ[ip1][jp1][kp1] * zR,
 
                         d2FdXdY[i][j][k] * xRyR, d2FdXdY[ip1][j][k] * xRyR,
                         d2FdXdY[i][jp1][k] * xRyR, d2FdXdY[ip1][jp1][k] * xRyR,
                         d2FdXdY[i][j][kp1] * xRyR, d2FdXdY[ip1][j][kp1] * xRyR,
                         d2FdXdY[i][jp1][kp1] * xRyR, d2FdXdY[ip1][jp1][kp1] * xRyR,
 
                         d2FdXdZ[i][j][k] * xRzR, d2FdXdZ[ip1][j][k] * xRzR,
                         d2FdXdZ[i][jp1][k] * xRzR, d2FdXdZ[ip1][jp1][k] * xRzR,
                         d2FdXdZ[i][j][kp1] * xRzR, d2FdXdZ[ip1][j][kp1] * xRzR,
                         d2FdXdZ[i][jp1][kp1] * xRzR, d2FdXdZ[ip1][jp1][kp1] * xRzR,
 
                         d2FdYdZ[i][j][k] * yRzR, d2FdYdZ[ip1][j][k] * yRzR,
                         d2FdYdZ[i][jp1][k] * yRzR, d2FdYdZ[ip1][jp1][k] * yRzR,
                         d2FdYdZ[i][j][kp1] * yRzR, d2FdYdZ[ip1][j][kp1] * yRzR,
                         d2FdYdZ[i][jp1][kp1] * yRzR, d2FdYdZ[ip1][jp1][kp1] * yRzR,
 
                         d3FdXdYdZ[i][j][k] * xRyRzR, d3FdXdYdZ[ip1][j][k] * xRyRzR,
                         d3FdXdYdZ[i][jp1][k] * xRyRzR, d3FdXdYdZ[ip1][jp1][k] * xRyRzR,
                         d3FdXdYdZ[i][j][kp1] * xRyRzR, d3FdXdYdZ[ip1][j][kp1] * xRyRzR,
                         d3FdXdYdZ[i][jp1][kp1] * xRyRzR, d3FdXdYdZ[ip1][jp1][kp1] * xRyRzR,
                     };
 
                     splines[i][j][k] = new TricubicFunction(computeCoefficients(beta));
                 }
             }
         }
     }
 
     /**
      * {@inheritDoc}
      *
      * @throws OutOfRangeException if any of the variables is outside its interpolation range.
      */
     @Override
     public double value(double x, double y, double z)
         throws OutOfRangeException {
         final int i = searchIndex(x, xval);
         if (i == -1) {
             throw new OutOfRangeException(x, xval[0], xval[xval.length - 1]);
         }
         final int j = searchIndex(y, yval);
         if (j == -1) {
             throw new OutOfRangeException(y, yval[0], yval[yval.length - 1]);
         }
         final int k = searchIndex(z, zval);
         if (k == -1) {
             throw new OutOfRangeException(z, zval[0], zval[zval.length - 1]);
         }
 
         final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);
         final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);
         final double zN = (z - zval[k]) / (zval[k + 1] - zval[k]);
 
         return splines[i][j][k].value(xN, yN, zN);
     }
 
     /**
      * Indicates whether a point is within the interpolation range.
      *
      * @param x First coordinate.
      * @param y Second coordinate.
      * @param z Third coordinate.
      * @return {@code true} if (x, y, z) is a valid point.
      */
     public boolean isValidPoint(double x, double y, double z) {
         return !(x < xval[0] ||
             x > xval[xval.length - 1] ||
             y < yval[0] ||
             y > yval[yval.length - 1] ||
             z < zval[0] ||
             z > zval[zval.length - 1]);
     }
 
     /**
      * @param c Coordinate.
      * @param val Coordinate samples.
      * @return the index in {@code val} corresponding to the interval containing {@code c}, or {@code -1}
      *   if {@code c} is out of the range defined by the end values of {@code val}.
      */
     private int searchIndex(double c, double[] val) {
         if (c < val[0]) {
             return -1;
         }
 
         final int max = val.length;
         for (int i = 1; i < max; i++) {
             if (c <= val[i]) {
                 return i - 1;
             }
         }
 
         return -1;
     }
 
     /**
      * Compute the spline coefficients from the list of function values and
      * function partial derivatives values at the four corners of a grid
      * element. They must be specified in the following order:
      * <ul>
      *  <li>f(0,0,0)</li>
      *  <li>f(1,0,0)</li>
      *  <li>f(0,1,0)</li>
      *  <li>f(1,1,0)</li>
      *  <li>f(0,0,1)</li>
      *  <li>f(1,0,1)</li>
      *  <li>f(0,1,1)</li>
      *  <li>f(1,1,1)</li>
      *
      *  <li>f<sub>x</sub>(0,0,0)</li>
      *  <li>... <em>(same order as above)</em></li>
      *  <li>f<sub>x</sub>(1,1,1)</li>
      *
      *  <li>f<sub>y</sub>(0,0,0)</li>
      *  <li>... <em>(same order as above)</em></li>
      *  <li>f<sub>y</sub>(1,1,1)</li>
      *
      *  <li>f<sub>z</sub>(0,0,0)</li>
      *  <li>... <em>(same order as above)</em></li>
      *  <li>f<sub>z</sub>(1,1,1)</li>
      *
      *  <li>f<sub>xy</sub>(0,0,0)</li>
      *  <li>... <em>(same order as above)</em></li>
      *  <li>f<sub>xy</sub>(1,1,1)</li>
      *
      *  <li>f<sub>xz</sub>(0,0,0)</li>
      *  <li>... <em>(same order as above)</em></li>
      *  <li>f<sub>xz</sub>(1,1,1)</li>
      *
      *  <li>f<sub>yz</sub>(0,0,0)</li>
      *  <li>... <em>(same order as above)</em></li>
      *  <li>f<sub>yz</sub>(1,1,1)</li>
      *
      *  <li>f<sub>xyz</sub>(0,0,0)</li>
      *  <li>... <em>(same order as above)</em></li>
      *  <li>f<sub>xyz</sub>(1,1,1)</li>
      * </ul>
      * where the subscripts indicate the partial derivative with respect to
      * the corresponding variable(s).
      *
      * @param beta List of function values and function partial derivatives values.
      * @return the spline coefficients.
      */
     private double[] computeCoefficients(double[] beta) {
         final int sz = 64;
         final double[] a = new double[sz];
 
         for (int i = 0; i < sz; i++) {
             double result = 0;
             final double[] row = AINV[i];
             for (int j = 0; j < sz; j++) {
                 result += row[j] * beta[j];
             }
             a[i] = result;
         }
 
         return a;
     }
 }
 
 /**
  * 3D-spline function.
  *
  */
 class TricubicFunction
     implements TrivariateFunction {
     /** Number of points. */
     private static final short N = 4;
     /** Coefficients. */
     private final double[][][] a = new double[N][N][N];
 
     /**
      * @param aV List of spline coefficients.
      */
     TricubicFunction(double[] aV) {
         for (int i = 0; i < N; i++) {
             for (int j = 0; j < N; j++) {
                 for (int k = 0; k < N; k++) {
                     a[i][j][k] = aV[i + N * (j + N * k)];
                 }
             }
         }
     }
 
     /**
      * @param x x-coordinate of the interpolation point.
      * @param y y-coordinate of the interpolation point.
      * @param z z-coordinate of the interpolation point.
      * @return the interpolated value.
      * @throws OutOfRangeException if {@code x}, {@code y} or
      * {@code z} are not in the interval {@code [0, 1]}.
      */
     @Override
     public double value(double x, double y, double z) throws OutOfRangeException {
         if (x < 0 || x > 1) {
             throw new OutOfRangeException(x, 0, 1);
         }
         if (y < 0 || y > 1) {
             throw new OutOfRangeException(y, 0, 1);
         }
         if (z < 0 || z > 1) {
             throw new OutOfRangeException(z, 0, 1);
         }
 
         final double x2 = x * x;
         final double x3 = x2 * x;
         final double[] pX = { 1, x, x2, x3 };
 
         final double y2 = y * y;
         final double y3 = y2 * y;
         final double[] pY = { 1, y, y2, y3 };
 
         final double z2 = z * z;
         final double z3 = z2 * z;
         final double[] pZ = { 1, z, z2, z3 };
 
         double result = 0;
         for (int i = 0; i < N; i++) {
             for (int j = 0; j < N; j++) {
                 for (int k = 0; k < N; k++) {
                     result += a[i][j][k] * pX[i] * pY[j] * pZ[k];
                 }
             }
         }
 
         return result;
     }
 }