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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* 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
*
* tricubic spline interpolation, as proposed in
*
* Tricubic interpolation in three dimensions,
* F. Lekien and J. Marsden,
* Int. J. Numer. Meth. Eng 2005; 63:455-471
*
*
* @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.
*/
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) {
if (x < xval[0] ||
x > xval[xval.length - 1] ||
y < yval[0] ||
y > yval[yval.length - 1] ||
z < zval[0] ||
z > zval[zval.length - 1]) {
return false;
} else {
return true;
}
}
/**
* @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:
*
* - f(0,0,0)
* - f(1,0,0)
* - f(0,1,0)
* - f(1,1,0)
* - f(0,0,1)
* - f(1,0,1)
* - f(0,1,1)
* - f(1,1,1)
*
* - fx(0,0,0)
* - ... (same order as above)
* - fx(1,1,1)
*
* - fy(0,0,0)
* - ... (same order as above)
* - fy(1,1,1)
*
* - fz(0,0,0)
* - ... (same order as above)
* - fz(1,1,1)
*
* - fxy(0,0,0)
* - ... (same order as above)
* - fxy(1,1,1)
*
* - fxz(0,0,0)
* - ... (same order as above)
* - fxz(1,1,1)
*
* - fyz(0,0,0)
* - ... (same order as above)
* - fyz(1,1,1)
*
* - fxyz(0,0,0)
* - ... (same order as above)
* - fxyz(1,1,1)
*
* 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]}.
*/
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;
}
}