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 */ 017 package org.apache.commons.math3.analysis.interpolation; 018 019 import org.apache.commons.math3.analysis.TrivariateFunction; 020 import org.apache.commons.math3.exception.DimensionMismatchException; 021 import org.apache.commons.math3.exception.NoDataException; 022 import org.apache.commons.math3.exception.OutOfRangeException; 023 import org.apache.commons.math3.exception.NonMonotonicSequenceException; 024 import 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 * <quote> 031 * Tricubic interpolation in three dimensions<br/> 032 * F. Lekien and J. Marsden<br/> 033 * <em>Int. J. Numer. Meth. Engng</em> 2005; <b>63</b>:455-471 034 * </quote> 035 * 036 * @since 2.2 037 * @version $Id: TricubicSplineInterpolatingFunction.java 1385314 2012-09-16 16:35:49Z tn $ 038 */ 039 public class TricubicSplineInterpolatingFunction 040 implements TrivariateFunction { 041 /** 042 * Matrix to compute the spline coefficients from the function values 043 * and function derivatives values 044 */ 045 private static final double[][] AINV = { 046 { 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 }, 047 { 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 }, 048 { -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 }, 049 { 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 }, 050 { 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 }, 051 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 }, 052 { 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 }, 053 { 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 }, 054 { -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 }, 055 { 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 }, 056 { 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 }, 057 { -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 }, 058 { 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 }, 059 { 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 }, 060 { -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 }, 061 { 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 }, 062 { 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 }, 063 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 }, 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,-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 }, 065 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-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 }, 066 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 }, 067 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 }, 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,-3,3,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0 }, 069 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,1,1,0,0,0,0,0,0 }, 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,-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 }, 071 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0 }, 072 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9,-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 }, 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,-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 }, 074 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,-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 }, 075 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0 }, 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,-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 }, 077 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-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 }, 078 {-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 }, 079 { 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 }, 080 { 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 }, 081 { -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 }, 082 { 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 }, 083 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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 }, 084 { 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 }, 085 { 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 }, 086 { 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 }, 087 { 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 }, 088 { -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 }, 089 { 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 }, 090 { -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 }, 091 { 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 }, 092 { 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 }, 093 { -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 }, 094 { 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 }, 095 { 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 }, 096 { -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 }, 097 { 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 }, 098 { 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 }, 099 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,-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 }, 100 { 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 }, 101 { 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 }, 102 { -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 }, 103 { 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 }, 104 { 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 }, 105 { -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 }, 106 { 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 }, 107 { 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 }, 108 { -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 }, 109 { 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 } 110 }; 111 112 /** Samples x-coordinates */ 113 private final double[] xval; 114 /** Samples y-coordinates */ 115 private final double[] yval; 116 /** Samples z-coordinates */ 117 private final double[] zval; 118 /** Set of cubic splines pacthing the whole data grid */ 119 private final TricubicSplineFunction[][][] splines; 120 121 /** 122 * @param x Sample values of the x-coordinate, in increasing order. 123 * @param y Sample values of the y-coordinate, in increasing order. 124 * @param z Sample values of the y-coordinate, in increasing order. 125 * @param f Values of the function on every grid point. 126 * @param dFdX Values of the partial derivative of function with respect to x on every grid point. 127 * @param dFdY Values of the partial derivative of function with respect to y on every grid point. 128 * @param dFdZ Values of the partial derivative of function with respect to z on every grid point. 129 * @param d2FdXdY Values of the cross partial derivative of function on every grid point. 130 * @param d2FdXdZ Values of the cross partial derivative of function on every grid point. 131 * @param d2FdYdZ Values of the cross partial derivative of function on every grid point. 132 * @param d3FdXdYdZ Values of the cross partial derivative of function on every grid point. 133 * @throws NoDataException if any of the arrays has zero length. 134 * @throws DimensionMismatchException if the various arrays do not contain the expected number of elements. 135 * @throws NonMonotonicSequenceException if {@code x}, {@code y} or {@code z} are not strictly increasing. 136 */ 137 public TricubicSplineInterpolatingFunction(double[] x, 138 double[] y, 139 double[] z, 140 double[][][] f, 141 double[][][] dFdX, 142 double[][][] dFdY, 143 double[][][] dFdZ, 144 double[][][] d2FdXdY, 145 double[][][] d2FdXdZ, 146 double[][][] d2FdYdZ, 147 double[][][] d3FdXdYdZ) 148 throws NoDataException, 149 DimensionMismatchException, 150 NonMonotonicSequenceException { 151 final int xLen = x.length; 152 final int yLen = y.length; 153 final int zLen = z.length; 154 155 if (xLen == 0 || yLen == 0 || z.length == 0 || f.length == 0 || f[0].length == 0) { 156 throw new NoDataException(); 157 } 158 if (xLen != f.length) { 159 throw new DimensionMismatchException(xLen, f.length); 160 } 161 if (xLen != dFdX.length) { 162 throw new DimensionMismatchException(xLen, dFdX.length); 163 } 164 if (xLen != dFdY.length) { 165 throw new DimensionMismatchException(xLen, dFdY.length); 166 } 167 if (xLen != dFdZ.length) { 168 throw new DimensionMismatchException(xLen, dFdZ.length); 169 } 170 if (xLen != d2FdXdY.length) { 171 throw new DimensionMismatchException(xLen, d2FdXdY.length); 172 } 173 if (xLen != d2FdXdZ.length) { 174 throw new DimensionMismatchException(xLen, d2FdXdZ.length); 175 } 176 if (xLen != d2FdYdZ.length) { 177 throw new DimensionMismatchException(xLen, d2FdYdZ.length); 178 } 179 if (xLen != d3FdXdYdZ.length) { 180 throw new DimensionMismatchException(xLen, d3FdXdYdZ.length); 181 } 182 183 MathArrays.checkOrder(x); 184 MathArrays.checkOrder(y); 185 MathArrays.checkOrder(z); 186 187 xval = x.clone(); 188 yval = y.clone(); 189 zval = z.clone(); 190 191 final int lastI = xLen - 1; 192 final int lastJ = yLen - 1; 193 final int lastK = zLen - 1; 194 splines = new TricubicSplineFunction[lastI][lastJ][lastK]; 195 196 for (int i = 0; i < lastI; i++) { 197 if (f[i].length != yLen) { 198 throw new DimensionMismatchException(f[i].length, yLen); 199 } 200 if (dFdX[i].length != yLen) { 201 throw new DimensionMismatchException(dFdX[i].length, yLen); 202 } 203 if (dFdY[i].length != yLen) { 204 throw new DimensionMismatchException(dFdY[i].length, yLen); 205 } 206 if (dFdZ[i].length != yLen) { 207 throw new DimensionMismatchException(dFdZ[i].length, yLen); 208 } 209 if (d2FdXdY[i].length != yLen) { 210 throw new DimensionMismatchException(d2FdXdY[i].length, yLen); 211 } 212 if (d2FdXdZ[i].length != yLen) { 213 throw new DimensionMismatchException(d2FdXdZ[i].length, yLen); 214 } 215 if (d2FdYdZ[i].length != yLen) { 216 throw new DimensionMismatchException(d2FdYdZ[i].length, yLen); 217 } 218 if (d3FdXdYdZ[i].length != yLen) { 219 throw new DimensionMismatchException(d3FdXdYdZ[i].length, yLen); 220 } 221 222 final int ip1 = i + 1; 223 for (int j = 0; j < lastJ; j++) { 224 if (f[i][j].length != zLen) { 225 throw new DimensionMismatchException(f[i][j].length, zLen); 226 } 227 if (dFdX[i][j].length != zLen) { 228 throw new DimensionMismatchException(dFdX[i][j].length, zLen); 229 } 230 if (dFdY[i][j].length != zLen) { 231 throw new DimensionMismatchException(dFdY[i][j].length, zLen); 232 } 233 if (dFdZ[i][j].length != zLen) { 234 throw new DimensionMismatchException(dFdZ[i][j].length, zLen); 235 } 236 if (d2FdXdY[i][j].length != zLen) { 237 throw new DimensionMismatchException(d2FdXdY[i][j].length, zLen); 238 } 239 if (d2FdXdZ[i][j].length != zLen) { 240 throw new DimensionMismatchException(d2FdXdZ[i][j].length, zLen); 241 } 242 if (d2FdYdZ[i][j].length != zLen) { 243 throw new DimensionMismatchException(d2FdYdZ[i][j].length, zLen); 244 } 245 if (d3FdXdYdZ[i][j].length != zLen) { 246 throw new DimensionMismatchException(d3FdXdYdZ[i][j].length, zLen); 247 } 248 249 final int jp1 = j + 1; 250 for (int k = 0; k < lastK; k++) { 251 final int kp1 = k + 1; 252 253 final double[] beta = new double[] { 254 f[i][j][k], f[ip1][j][k], 255 f[i][jp1][k], f[ip1][jp1][k], 256 f[i][j][kp1], f[ip1][j][kp1], 257 f[i][jp1][kp1], f[ip1][jp1][kp1], 258 259 dFdX[i][j][k], dFdX[ip1][j][k], 260 dFdX[i][jp1][k], dFdX[ip1][jp1][k], 261 dFdX[i][j][kp1], dFdX[ip1][j][kp1], 262 dFdX[i][jp1][kp1], dFdX[ip1][jp1][kp1], 263 264 dFdY[i][j][k], dFdY[ip1][j][k], 265 dFdY[i][jp1][k], dFdY[ip1][jp1][k], 266 dFdY[i][j][kp1], dFdY[ip1][j][kp1], 267 dFdY[i][jp1][kp1], dFdY[ip1][jp1][kp1], 268 269 dFdZ[i][j][k], dFdZ[ip1][j][k], 270 dFdZ[i][jp1][k], dFdZ[ip1][jp1][k], 271 dFdZ[i][j][kp1], dFdZ[ip1][j][kp1], 272 dFdZ[i][jp1][kp1], dFdZ[ip1][jp1][kp1], 273 274 d2FdXdY[i][j][k], d2FdXdY[ip1][j][k], 275 d2FdXdY[i][jp1][k], d2FdXdY[ip1][jp1][k], 276 d2FdXdY[i][j][kp1], d2FdXdY[ip1][j][kp1], 277 d2FdXdY[i][jp1][kp1], d2FdXdY[ip1][jp1][kp1], 278 279 d2FdXdZ[i][j][k], d2FdXdZ[ip1][j][k], 280 d2FdXdZ[i][jp1][k], d2FdXdZ[ip1][jp1][k], 281 d2FdXdZ[i][j][kp1], d2FdXdZ[ip1][j][kp1], 282 d2FdXdZ[i][jp1][kp1], d2FdXdZ[ip1][jp1][kp1], 283 284 d2FdYdZ[i][j][k], d2FdYdZ[ip1][j][k], 285 d2FdYdZ[i][jp1][k], d2FdYdZ[ip1][jp1][k], 286 d2FdYdZ[i][j][kp1], d2FdYdZ[ip1][j][kp1], 287 d2FdYdZ[i][jp1][kp1], d2FdYdZ[ip1][jp1][kp1], 288 289 d3FdXdYdZ[i][j][k], d3FdXdYdZ[ip1][j][k], 290 d3FdXdYdZ[i][jp1][k], d3FdXdYdZ[ip1][jp1][k], 291 d3FdXdYdZ[i][j][kp1], d3FdXdYdZ[ip1][j][kp1], 292 d3FdXdYdZ[i][jp1][kp1], d3FdXdYdZ[ip1][jp1][kp1], 293 }; 294 295 splines[i][j][k] = new TricubicSplineFunction(computeSplineCoefficients(beta)); 296 } 297 } 298 } 299 } 300 301 /** 302 * {@inheritDoc} 303 * 304 * @throws OutOfRangeException if any of the variables is outside its interpolation range. 305 */ 306 public double value(double x, double y, double z) 307 throws OutOfRangeException { 308 final int i = searchIndex(x, xval); 309 if (i == -1) { 310 throw new OutOfRangeException(x, xval[0], xval[xval.length - 1]); 311 } 312 final int j = searchIndex(y, yval); 313 if (j == -1) { 314 throw new OutOfRangeException(y, yval[0], yval[yval.length - 1]); 315 } 316 final int k = searchIndex(z, zval); 317 if (k == -1) { 318 throw new OutOfRangeException(z, zval[0], zval[zval.length - 1]); 319 } 320 321 final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]); 322 final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]); 323 final double zN = (z - zval[k]) / (zval[k + 1] - zval[k]); 324 325 return splines[i][j][k].value(xN, yN, zN); 326 } 327 328 /** 329 * @param c Coordinate. 330 * @param val Coordinate samples. 331 * @return the index in {@code val} corresponding to the interval containing {@code c}, or {@code -1} 332 * if {@code c} is out of the range defined by the end values of {@code val}. 333 */ 334 private int searchIndex(double c, double[] val) { 335 if (c < val[0]) { 336 return -1; 337 } 338 339 final int max = val.length; 340 for (int i = 1; i < max; i++) { 341 if (c <= val[i]) { 342 return i - 1; 343 } 344 } 345 346 return -1; 347 } 348 349 /** 350 * Compute the spline coefficients from the list of function values and 351 * function partial derivatives values at the four corners of a grid 352 * element. They must be specified in the following order: 353 * <ul> 354 * <li>f(0,0,0)</li> 355 * <li>f(1,0,0)</li> 356 * <li>f(0,1,0)</li> 357 * <li>f(1,1,0)</li> 358 * <li>f(0,0,1)</li> 359 * <li>f(1,0,1)</li> 360 * <li>f(0,1,1)</li> 361 * <li>f(1,1,1)</li> 362 * 363 * <li>f<sub>x</sub>(0,0,0)</li> 364 * <li>... <em>(same order as above)</em></li> 365 * <li>f<sub>x</sub>(1,1,1)</li> 366 * 367 * <li>f<sub>y</sub>(0,0,0)</li> 368 * <li>... <em>(same order as above)</em></li> 369 * <li>f<sub>y</sub>(1,1,1)</li> 370 * 371 * <li>f<sub>z</sub>(0,0,0)</li> 372 * <li>... <em>(same order as above)</em></li> 373 * <li>f<sub>z</sub>(1,1,1)</li> 374 * 375 * <li>f<sub>xy</sub>(0,0,0)</li> 376 * <li>... <em>(same order as above)</em></li> 377 * <li>f<sub>xy</sub>(1,1,1)</li> 378 * 379 * <li>f<sub>xz</sub>(0,0,0)</li> 380 * <li>... <em>(same order as above)</em></li> 381 * <li>f<sub>xz</sub>(1,1,1)</li> 382 * 383 * <li>f<sub>yz</sub>(0,0,0)</li> 384 * <li>... <em>(same order as above)</em></li> 385 * <li>f<sub>yz</sub>(1,1,1)</li> 386 * 387 * <li>f<sub>xyz</sub>(0,0,0)</li> 388 * <li>... <em>(same order as above)</em></li> 389 * <li>f<sub>xyz</sub>(1,1,1)</li> 390 * </ul> 391 * where the subscripts indicate the partial derivative with respect to 392 * the corresponding variable(s). 393 * 394 * @param beta List of function values and function partial derivatives values. 395 * @return the spline coefficients. 396 */ 397 private double[] computeSplineCoefficients(double[] beta) { 398 final int sz = 64; 399 final double[] a = new double[sz]; 400 401 for (int i = 0; i < sz; i++) { 402 double result = 0; 403 final double[] row = AINV[i]; 404 for (int j = 0; j < sz; j++) { 405 result += row[j] * beta[j]; 406 } 407 a[i] = result; 408 } 409 410 return a; 411 } 412 } 413 414 /** 415 * 3D-spline function. 416 * 417 * @version $Id: TricubicSplineInterpolatingFunction.java 1385314 2012-09-16 16:35:49Z tn $ 418 */ 419 class 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 public 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 }