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Java example source code file (TricubicSplineInterpolatingFunction.java)

This example Java source code file (TricubicSplineInterpolatingFunction.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

ainv, deprecated, dimensionmismatchexception, nodataexception, nonmonotonicsequenceexception, outofrangeexception, tricubicsplinefunction, tricubicsplineinterpolatingfunction, trivariatefunction

The TricubicSplineInterpolatingFunction.java Java example source code

/*
 * 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.math3.analysis.interpolation;

import org.apache.commons.math3.analysis.TrivariateFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.util.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,
 *  F. Lekien and J. Marsden,
 *  <em>Int. J. Numer. Meth. Engng 2005; 63:455-471
 * </blockquote>
 *
 * @since 2.2
 * @deprecated To be removed in 4.0 (see MATH-1166).
 */
@Deprecated
public class TricubicSplineInterpolatingFunction
    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 pacthing the whole data grid */
    private final TricubicSplineFunction[][][] 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 TricubicSplineInterpolatingFunction(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 TricubicSplineFunction[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;
            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;
                for (int k = 0; k < lastK; k++) {
                    final int kp1 = k + 1;

                    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], dFdX[ip1][j][k],
                        dFdX[i][jp1][k], dFdX[ip1][jp1][k],
                        dFdX[i][j][kp1], dFdX[ip1][j][kp1],
                        dFdX[i][jp1][kp1], dFdX[ip1][jp1][kp1],

                        dFdY[i][j][k], dFdY[ip1][j][k],
                        dFdY[i][jp1][k], dFdY[ip1][jp1][k],
                        dFdY[i][j][kp1], dFdY[ip1][j][kp1],
                        dFdY[i][jp1][kp1], dFdY[ip1][jp1][kp1],

                        dFdZ[i][j][k], dFdZ[ip1][j][k],
                        dFdZ[i][jp1][k], dFdZ[ip1][jp1][k],
                        dFdZ[i][j][kp1], dFdZ[ip1][j][kp1],
                        dFdZ[i][jp1][kp1], dFdZ[ip1][jp1][kp1],

                        d2FdXdY[i][j][k], d2FdXdY[ip1][j][k],
                        d2FdXdY[i][jp1][k], d2FdXdY[ip1][jp1][k],
                        d2FdXdY[i][j][kp1], d2FdXdY[ip1][j][kp1],
                        d2FdXdY[i][jp1][kp1], d2FdXdY[ip1][jp1][kp1],

                        d2FdXdZ[i][j][k], d2FdXdZ[ip1][j][k],
                        d2FdXdZ[i][jp1][k], d2FdXdZ[ip1][jp1][k],
                        d2FdXdZ[i][j][kp1], d2FdXdZ[ip1][j][kp1],
                        d2FdXdZ[i][jp1][kp1], d2FdXdZ[ip1][jp1][kp1],

                        d2FdYdZ[i][j][k], d2FdYdZ[ip1][j][k],
                        d2FdYdZ[i][jp1][k], d2FdYdZ[ip1][jp1][k],
                        d2FdYdZ[i][j][kp1], d2FdYdZ[ip1][j][kp1],
                        d2FdYdZ[i][jp1][kp1], d2FdYdZ[ip1][jp1][kp1],

                        d3FdXdYdZ[i][j][k], d3FdXdYdZ[ip1][j][k],
                        d3FdXdYdZ[i][jp1][k], d3FdXdYdZ[ip1][jp1][k],
                        d3FdXdYdZ[i][j][kp1], d3FdXdYdZ[ip1][j][kp1],
                        d3FdXdYdZ[i][jp1][kp1], d3FdXdYdZ[ip1][jp1][kp1],
                    };

                    splines[i][j][k] = new TricubicSplineFunction(computeSplineCoefficients(beta));
                }
            }
        }
    }

    /**
     * {@inheritDoc}
     *
     * @throws OutOfRangeException if any of the variables is outside its interpolation range.
     */
    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);
    }

    /**
     * @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>f(1,0,0)
     *  <li>f(0,1,0)
     *  <li>f(1,1,0)
     *  <li>f(0,0,1)
     *  <li>f(1,0,1)
     *  <li>f(0,1,1)
     *  <li>f(1,1,1)
     *
     *  <li>fx(0,0,0)
     *  <li>... (same order as above)
     *  <li>fx(1,1,1)
     *
     *  <li>fy(0,0,0)
     *  <li>... (same order as above)
     *  <li>fy(1,1,1)
     *
     *  <li>fz(0,0,0)
     *  <li>... (same order as above)
     *  <li>fz(1,1,1)
     *
     *  <li>fxy(0,0,0)
     *  <li>... (same order as above)
     *  <li>fxy(1,1,1)
     *
     *  <li>fxz(0,0,0)
     *  <li>... (same order as above)
     *  <li>fxz(1,1,1)
     *
     *  <li>fyz(0,0,0)
     *  <li>... (same order as above)
     *  <li>fyz(1,1,1)
     *
     *  <li>fxyz(0,0,0)
     *  <li>... (same order as above)
     *  <li>fxyz(1,1,1)
     * </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[] computeSplineCoefficients(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 TricubicSplineFunction
    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.
     */
    TricubicSplineFunction(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]}.
     */
    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;
    }
}

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