source: src/main/java/agents/anac/y2019/harddealer/math3/analysis/interpolation/TricubicSplineInterpolatingFunction.java

Last change on this file was 204, checked in by Katsuhide Fujita, 5 years ago

Fixed errors of ANAC2019 agents
  • Property svn:executable set to *
File size: 25.3 KB
Line 
1/*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17package agents.anac.y2019.harddealer.math3.analysis.interpolation;
18
19import agents.anac.y2019.harddealer.math3.analysis.TrivariateFunction;
20import agents.anac.y2019.harddealer.math3.exception.DimensionMismatchException;
21import agents.anac.y2019.harddealer.math3.exception.NoDataException;
22import agents.anac.y2019.harddealer.math3.exception.NonMonotonicSequenceException;
23import agents.anac.y2019.harddealer.math3.exception.OutOfRangeException;
24import agents.anac.y2019.harddealer.math3.util.MathArrays;
25
26/**
27 * Function that implements the
28 * <a href="http://en.wikipedia.org/wiki/Tricubic_interpolation">
29 * tricubic spline interpolation</a>, as proposed in
30 * <blockquote>
31 * Tricubic interpolation in three dimensions,
32 * F. Lekien and J. Marsden,
33 * <em>Int. J. Numer. Meth. Engng</em> 2005; <b>63</b>:455-471
34 * </blockquote>
35 *
36 * @since 2.2
37 * @deprecated To be removed in 4.0 (see MATH-1166).
38 */
39@Deprecated
40public class TricubicSplineInterpolatingFunction
41 implements TrivariateFunction {
42 /**
43 * Matrix to compute the spline coefficients from the function values
44 * and function derivatives values
45 */
46 private static final double[][] AINV = {
47 { 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 },
48 { 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 },
49 { -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 },
50 { 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 },
51 { 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 },
52 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
53 { 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 },
54 { 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 },
55 { -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 },
56 { 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 },
57 { 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 },
58 { -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 },
59 { 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 },
60 { 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 },
61 { -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 },
62 { 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 },
63 { 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 },
64 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
65 { 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 },
66 { 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 },
67 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
68 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 },
69 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,3,0,0,0,0,0,0,-2,-1,0,0,0,0,0,0 },
70 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,1,1,0,0,0,0,0,0 },
71 { 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 },
72 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-1,0,0,0,0,0 },
73 { 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 },
74 { 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 },
75 { 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 },
76 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0 },
77 { 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 },
78 { 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 },
79 {-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 },
80 { 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 },
81 { 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 },
82 { -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 },
83 { 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 },
84 { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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 },
85 { 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 },
86 { 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 },
87 { 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 },
88 { 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 },
89 { -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 },
90 { 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 },
91 { -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 },
92 { 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 },
93 { 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 },
94 { -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 },
95 { 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 },
96 { 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 },
97 { -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 },
98 { 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 },
99 { 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}
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