001/* 002 * Licensed to the Apache Software Foundation (ASF) under one or more 003 * contributor license agreements. See the NOTICE file distributed with 004 * this work for additional information regarding copyright ownership. 005 * The ASF licenses this file to You under the Apache License, Version 2.0 006 * (the "License"); you may not use this file except in compliance with 007 * the License. You may obtain a copy of the License at 008 * 009 * http://www.apache.org/licenses/LICENSE-2.0 010 * 011 * Unless required by applicable law or agreed to in writing, software 012 * distributed under the License is distributed on an "AS IS" BASIS, 013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 014 * See the License for the specific language governing permissions and 015 * limitations under the License. 016 */ 017package org.apache.commons.math3.analysis.interpolation; 018 019import org.apache.commons.math3.analysis.TrivariateFunction; 020import org.apache.commons.math3.exception.DimensionMismatchException; 021import org.apache.commons.math3.exception.NoDataException; 022import org.apache.commons.math3.exception.NonMonotonicSequenceException; 023import org.apache.commons.math3.exception.OutOfRangeException; 024import org.apache.commons.math3.util.MathArrays; 025 026/** 027 * Function that implements the 028 * <a href="http://en.wikipedia.org/wiki/Tricubic_interpolation"> 029 * tricubic spline interpolation</a>, as proposed in 030 * <blockquote> 031 * Tricubic interpolation in three dimensions, 032 * F. Lekien and J. Marsden, 033 * <em>Int. J. Numer. Meth. Engng</em> 2005; <b>63</b>:455-471 034 * </blockquote> 035 * 036 * @since 2.2 037 * @deprecated To be removed in 4.0 (see MATH-1166). 038 */ 039@Deprecated 040public class TricubicSplineInterpolatingFunction 041 implements TrivariateFunction { 042 /** 043 * Matrix to compute the spline coefficients from the function values 044 * and function derivatives values 045 */ 046 private static final double[][] AINV = { 047 { 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 }, 048 { 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 }, 049 { -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 }, 050 { 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 }, 051 { 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 }, 052 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 }, 053 { 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 }, 054 { 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 }, 055 { -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 }, 056 { 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 }, 057 { 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 }, 058 { -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 }, 059 { 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 }, 060 { 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 }, 061 { -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 }, 062 { 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 }, 063 { 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 }, 064 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 }, 065 { 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 }, 066 { 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 }, 067 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 }, 068 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 }, 069 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0 }, 070 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,1,1,0,0,0,0,0,0 }, 071 { 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 }, 072 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0 }, 073 { 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 }, 074 { 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 }, 075 { 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 }, 076 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0 }, 077 { 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 }, 078 { 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 }, 079 {-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 }, 080 { 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 }, 081 { 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 }, 082 { -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 }, 083 { 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 }, 084 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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 }, 085 { 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 }, 086 { 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 }, 087 { 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 }, 088 { 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 }, 089 { -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 }, 090 { 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 }, 091 { -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 }, 092 { 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 }, 093 { 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 }, 094 { -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 }, 095 { 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 }, 096 { 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 }, 097 { -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 }, 098 { 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 }, 099 { 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 }, 100 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,-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 }, 101 { 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 }, 102 { 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 }, 103 { -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 }, 104 { 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 }, 105 { 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 }, 106 { -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 }, 107 { 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 }, 108 { 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 }, 109 { -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 }, 110 { 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 } 111 }; 112 113 /** Samples x-coordinates */ 114 private final double[] xval; 115 /** Samples y-coordinates */ 116 private final double[] yval; 117 /** Samples z-coordinates */ 118 private final double[] zval; 119 /** Set of cubic splines pacthing the whole data grid */ 120 private final TricubicSplineFunction[][][] splines; 121 122 /** 123 * @param x Sample values of the x-coordinate, in increasing order. 124 * @param y Sample values of the y-coordinate, in increasing order. 125 * @param z Sample values of the y-coordinate, in increasing order. 126 * @param f Values of the function on every grid point. 127 * @param dFdX Values of the partial derivative of function with respect to x on every grid point. 128 * @param dFdY Values of the partial derivative of function with respect to y on every grid point. 129 * @param dFdZ Values of the partial derivative of function with respect to z on every grid point. 130 * @param d2FdXdY Values of the cross partial derivative of function on every grid point. 131 * @param d2FdXdZ Values of the cross partial derivative of function on every grid point. 132 * @param d2FdYdZ Values of the cross partial derivative of function on every grid point. 133 * @param d3FdXdYdZ Values of the cross partial derivative of function on every grid point. 134 * @throws NoDataException if any of the arrays has zero length. 135 * @throws DimensionMismatchException if the various arrays do not contain the expected number of elements. 136 * @throws NonMonotonicSequenceException if {@code x}, {@code y} or {@code z} are not strictly increasing. 137 */ 138 public TricubicSplineInterpolatingFunction(double[] x, 139 double[] y, 140 double[] z, 141 double[][][] f, 142 double[][][] dFdX, 143 double[][][] dFdY, 144 double[][][] dFdZ, 145 double[][][] d2FdXdY, 146 double[][][] d2FdXdZ, 147 double[][][] d2FdYdZ, 148 double[][][] d3FdXdYdZ) 149 throws NoDataException, 150 DimensionMismatchException, 151 NonMonotonicSequenceException { 152 final int xLen = x.length; 153 final int yLen = y.length; 154 final int zLen = z.length; 155 156 if (xLen == 0 || yLen == 0 || z.length == 0 || f.length == 0 || f[0].length == 0) { 157 throw new NoDataException(); 158 } 159 if (xLen != f.length) { 160 throw new DimensionMismatchException(xLen, f.length); 161 } 162 if (xLen != dFdX.length) { 163 throw new DimensionMismatchException(xLen, dFdX.length); 164 } 165 if (xLen != dFdY.length) { 166 throw new DimensionMismatchException(xLen, dFdY.length); 167 } 168 if (xLen != dFdZ.length) { 169 throw new DimensionMismatchException(xLen, dFdZ.length); 170 } 171 if (xLen != d2FdXdY.length) { 172 throw new DimensionMismatchException(xLen, d2FdXdY.length); 173 } 174 if (xLen != d2FdXdZ.length) { 175 throw new DimensionMismatchException(xLen, d2FdXdZ.length); 176 } 177 if (xLen != d2FdYdZ.length) { 178 throw new DimensionMismatchException(xLen, d2FdYdZ.length); 179 } 180 if (xLen != d3FdXdYdZ.length) { 181 throw new DimensionMismatchException(xLen, d3FdXdYdZ.length); 182 } 183 184 MathArrays.checkOrder(x); 185 MathArrays.checkOrder(y); 186 MathArrays.checkOrder(z); 187 188 xval = x.clone(); 189 yval = y.clone(); 190 zval = z.clone(); 191 192 final int lastI = xLen - 1; 193 final int lastJ = yLen - 1; 194 final int lastK = zLen - 1; 195 splines = new TricubicSplineFunction[lastI][lastJ][lastK]; 196 197 for (int i = 0; i < lastI; i++) { 198 if (f[i].length != yLen) { 199 throw new DimensionMismatchException(f[i].length, yLen); 200 } 201 if (dFdX[i].length != yLen) { 202 throw new DimensionMismatchException(dFdX[i].length, yLen); 203 } 204 if (dFdY[i].length != yLen) { 205 throw new DimensionMismatchException(dFdY[i].length, yLen); 206 } 207 if (dFdZ[i].length != yLen) { 208 throw new DimensionMismatchException(dFdZ[i].length, yLen); 209 } 210 if (d2FdXdY[i].length != yLen) { 211 throw new DimensionMismatchException(d2FdXdY[i].length, yLen); 212 } 213 if (d2FdXdZ[i].length != yLen) { 214 throw new DimensionMismatchException(d2FdXdZ[i].length, yLen); 215 } 216 if (d2FdYdZ[i].length != yLen) { 217 throw new DimensionMismatchException(d2FdYdZ[i].length, yLen); 218 } 219 if (d3FdXdYdZ[i].length != yLen) { 220 throw new DimensionMismatchException(d3FdXdYdZ[i].length, yLen); 221 } 222 223 final int ip1 = i + 1; 224 for (int j = 0; j < lastJ; j++) { 225 if (f[i][j].length != zLen) { 226 throw new DimensionMismatchException(f[i][j].length, zLen); 227 } 228 if (dFdX[i][j].length != zLen) { 229 throw new DimensionMismatchException(dFdX[i][j].length, zLen); 230 } 231 if (dFdY[i][j].length != zLen) { 232 throw new DimensionMismatchException(dFdY[i][j].length, zLen); 233 } 234 if (dFdZ[i][j].length != zLen) { 235 throw new DimensionMismatchException(dFdZ[i][j].length, zLen); 236 } 237 if (d2FdXdY[i][j].length != zLen) { 238 throw new DimensionMismatchException(d2FdXdY[i][j].length, zLen); 239 } 240 if (d2FdXdZ[i][j].length != zLen) { 241 throw new DimensionMismatchException(d2FdXdZ[i][j].length, zLen); 242 } 243 if (d2FdYdZ[i][j].length != zLen) { 244 throw new DimensionMismatchException(d2FdYdZ[i][j].length, zLen); 245 } 246 if (d3FdXdYdZ[i][j].length != zLen) { 247 throw new DimensionMismatchException(d3FdXdYdZ[i][j].length, zLen); 248 } 249 250 final int jp1 = j + 1; 251 for (int k = 0; k < lastK; k++) { 252 final int kp1 = k + 1; 253 254 final double[] beta = new double[] { 255 f[i][j][k], f[ip1][j][k], 256 f[i][jp1][k], f[ip1][jp1][k], 257 f[i][j][kp1], f[ip1][j][kp1], 258 f[i][jp1][kp1], f[ip1][jp1][kp1], 259 260 dFdX[i][j][k], dFdX[ip1][j][k], 261 dFdX[i][jp1][k], dFdX[ip1][jp1][k], 262 dFdX[i][j][kp1], dFdX[ip1][j][kp1], 263 dFdX[i][jp1][kp1], dFdX[ip1][jp1][kp1], 264 265 dFdY[i][j][k], dFdY[ip1][j][k], 266 dFdY[i][jp1][k], dFdY[ip1][jp1][k], 267 dFdY[i][j][kp1], dFdY[ip1][j][kp1], 268 dFdY[i][jp1][kp1], dFdY[ip1][jp1][kp1], 269 270 dFdZ[i][j][k], dFdZ[ip1][j][k], 271 dFdZ[i][jp1][k], dFdZ[ip1][jp1][k], 272 dFdZ[i][j][kp1], dFdZ[ip1][j][kp1], 273 dFdZ[i][jp1][kp1], dFdZ[ip1][jp1][kp1], 274 275 d2FdXdY[i][j][k], d2FdXdY[ip1][j][k], 276 d2FdXdY[i][jp1][k], d2FdXdY[ip1][jp1][k], 277 d2FdXdY[i][j][kp1], d2FdXdY[ip1][j][kp1], 278 d2FdXdY[i][jp1][kp1], d2FdXdY[ip1][jp1][kp1], 279 280 d2FdXdZ[i][j][k], d2FdXdZ[ip1][j][k], 281 d2FdXdZ[i][jp1][k], d2FdXdZ[ip1][jp1][k], 282 d2FdXdZ[i][j][kp1], d2FdXdZ[ip1][j][kp1], 283 d2FdXdZ[i][jp1][kp1], d2FdXdZ[ip1][jp1][kp1], 284 285 d2FdYdZ[i][j][k], d2FdYdZ[ip1][j][k], 286 d2FdYdZ[i][jp1][k], d2FdYdZ[ip1][jp1][k], 287 d2FdYdZ[i][j][kp1], d2FdYdZ[ip1][j][kp1], 288 d2FdYdZ[i][jp1][kp1], d2FdYdZ[ip1][jp1][kp1], 289 290 d3FdXdYdZ[i][j][k], d3FdXdYdZ[ip1][j][k], 291 d3FdXdYdZ[i][jp1][k], d3FdXdYdZ[ip1][jp1][k], 292 d3FdXdYdZ[i][j][kp1], d3FdXdYdZ[ip1][j][kp1], 293 d3FdXdYdZ[i][jp1][kp1], d3FdXdYdZ[ip1][jp1][kp1], 294 }; 295 296 splines[i][j][k] = new TricubicSplineFunction(computeSplineCoefficients(beta)); 297 } 298 } 299 } 300 } 301 302 /** 303 * {@inheritDoc} 304 * 305 * @throws OutOfRangeException if any of the variables is outside its interpolation range. 306 */ 307 public double value(double x, double y, double z) 308 throws OutOfRangeException { 309 final int i = searchIndex(x, xval); 310 if (i == -1) { 311 throw new OutOfRangeException(x, xval[0], xval[xval.length - 1]); 312 } 313 final int j = searchIndex(y, yval); 314 if (j == -1) { 315 throw new OutOfRangeException(y, yval[0], yval[yval.length - 1]); 316 } 317 final int k = searchIndex(z, zval); 318 if (k == -1) { 319 throw new OutOfRangeException(z, zval[0], zval[zval.length - 1]); 320 } 321 322 final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]); 323 final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]); 324 final double zN = (z - zval[k]) / (zval[k + 1] - zval[k]); 325 326 return splines[i][j][k].value(xN, yN, zN); 327 } 328 329 /** 330 * @param c Coordinate. 331 * @param val Coordinate samples. 332 * @return the index in {@code val} corresponding to the interval containing {@code c}, or {@code -1} 333 * if {@code c} is out of the range defined by the end values of {@code val}. 334 */ 335 private int searchIndex(double c, double[] val) { 336 if (c < val[0]) { 337 return -1; 338 } 339 340 final int max = val.length; 341 for (int i = 1; i < max; i++) { 342 if (c <= val[i]) { 343 return i - 1; 344 } 345 } 346 347 return -1; 348 } 349 350 /** 351 * Compute the spline coefficients from the list of function values and 352 * function partial derivatives values at the four corners of a grid 353 * element. They must be specified in the following order: 354 * <ul> 355 * <li>f(0,0,0)</li> 356 * <li>f(1,0,0)</li> 357 * <li>f(0,1,0)</li> 358 * <li>f(1,1,0)</li> 359 * <li>f(0,0,1)</li> 360 * <li>f(1,0,1)</li> 361 * <li>f(0,1,1)</li> 362 * <li>f(1,1,1)</li> 363 * 364 * <li>f<sub>x</sub>(0,0,0)</li> 365 * <li>... <em>(same order as above)</em></li> 366 * <li>f<sub>x</sub>(1,1,1)</li> 367 * 368 * <li>f<sub>y</sub>(0,0,0)</li> 369 * <li>... <em>(same order as above)</em></li> 370 * <li>f<sub>y</sub>(1,1,1)</li> 371 * 372 * <li>f<sub>z</sub>(0,0,0)</li> 373 * <li>... <em>(same order as above)</em></li> 374 * <li>f<sub>z</sub>(1,1,1)</li> 375 * 376 * <li>f<sub>xy</sub>(0,0,0)</li> 377 * <li>... <em>(same order as above)</em></li> 378 * <li>f<sub>xy</sub>(1,1,1)</li> 379 * 380 * <li>f<sub>xz</sub>(0,0,0)</li> 381 * <li>... <em>(same order as above)</em></li> 382 * <li>f<sub>xz</sub>(1,1,1)</li> 383 * 384 * <li>f<sub>yz</sub>(0,0,0)</li> 385 * <li>... <em>(same order as above)</em></li> 386 * <li>f<sub>yz</sub>(1,1,1)</li> 387 * 388 * <li>f<sub>xyz</sub>(0,0,0)</li> 389 * <li>... <em>(same order as above)</em></li> 390 * <li>f<sub>xyz</sub>(1,1,1)</li> 391 * </ul> 392 * where the subscripts indicate the partial derivative with respect to 393 * the corresponding variable(s). 394 * 395 * @param beta List of function values and function partial derivatives values. 396 * @return the spline coefficients. 397 */ 398 private double[] computeSplineCoefficients(double[] beta) { 399 final int sz = 64; 400 final double[] a = new double[sz]; 401 402 for (int i = 0; i < sz; i++) { 403 double result = 0; 404 final double[] row = AINV[i]; 405 for (int j = 0; j < sz; j++) { 406 result += row[j] * beta[j]; 407 } 408 a[i] = result; 409 } 410 411 return a; 412 } 413} 414 415/** 416 * 3D-spline function. 417 * 418 */ 419class TricubicSplineFunction 420 implements TrivariateFunction { 421 /** Number of points. */ 422 private static final short N = 4; 423 /** Coefficients */ 424 private final double[][][] a = new double[N][N][N]; 425 426 /** 427 * @param aV List of spline coefficients. 428 */ 429 TricubicSplineFunction(double[] aV) { 430 for (int i = 0; i < N; i++) { 431 for (int j = 0; j < N; j++) { 432 for (int k = 0; k < N; k++) { 433 a[i][j][k] = aV[i + N * (j + N * k)]; 434 } 435 } 436 } 437 } 438 439 /** 440 * @param x x-coordinate of the interpolation point. 441 * @param y y-coordinate of the interpolation point. 442 * @param z z-coordinate of the interpolation point. 443 * @return the interpolated value. 444 * @throws OutOfRangeException if {@code x}, {@code y} or 445 * {@code z} are not in the interval {@code [0, 1]}. 446 */ 447 public double value(double x, double y, double z) 448 throws OutOfRangeException { 449 if (x < 0 || x > 1) { 450 throw new OutOfRangeException(x, 0, 1); 451 } 452 if (y < 0 || y > 1) { 453 throw new OutOfRangeException(y, 0, 1); 454 } 455 if (z < 0 || z > 1) { 456 throw new OutOfRangeException(z, 0, 1); 457 } 458 459 final double x2 = x * x; 460 final double x3 = x2 * x; 461 final double[] pX = { 1, x, x2, x3 }; 462 463 final double y2 = y * y; 464 final double y3 = y2 * y; 465 final double[] pY = { 1, y, y2, y3 }; 466 467 final double z2 = z * z; 468 final double z3 = z2 * z; 469 final double[] pZ = { 1, z, z2, z3 }; 470 471 double result = 0; 472 for (int i = 0; i < N; i++) { 473 for (int j = 0; j < N; j++) { 474 for (int k = 0; k < N; k++) { 475 result += a[i][j][k] * pX[i] * pY[j] * pZ[k]; 476 } 477 } 478 } 479 480 return result; 481 } 482}