| /* |
| * 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.math4.analysis.interpolation; |
| |
| import org.apache.commons.math4.analysis.TrivariateFunction; |
| import org.apache.commons.math4.exception.DimensionMismatchException; |
| import org.apache.commons.math4.exception.NoDataException; |
| import org.apache.commons.math4.exception.NonMonotonicSequenceException; |
| import org.apache.commons.math4.exception.OutOfRangeException; |
| import org.apache.commons.math4.util.MathArrays; |
| |
| /** |
| * Function that implements the |
| * <a href="http://en.wikipedia.org/wiki/Tricubic_interpolation"> |
| * tricubic spline interpolation</a>, as proposed in |
| * <blockquote> |
| * Tricubic interpolation in three dimensions<br> |
| * F. Lekien and J. Marsden<br> |
| * <em>Int. J. Numer. Meth. Eng</em> 2005; <b>63</b>:455-471<br> |
| * </blockquote> |
| * |
| * @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. |
| */ |
| @Override |
| 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: |
| * <ul> |
| * <li>f(0,0,0)</li> |
| * <li>f(1,0,0)</li> |
| * <li>f(0,1,0)</li> |
| * <li>f(1,1,0)</li> |
| * <li>f(0,0,1)</li> |
| * <li>f(1,0,1)</li> |
| * <li>f(0,1,1)</li> |
| * <li>f(1,1,1)</li> |
| * |
| * <li>f<sub>x</sub>(0,0,0)</li> |
| * <li>... <em>(same order as above)</em></li> |
| * <li>f<sub>x</sub>(1,1,1)</li> |
| * |
| * <li>f<sub>y</sub>(0,0,0)</li> |
| * <li>... <em>(same order as above)</em></li> |
| * <li>f<sub>y</sub>(1,1,1)</li> |
| * |
| * <li>f<sub>z</sub>(0,0,0)</li> |
| * <li>... <em>(same order as above)</em></li> |
| * <li>f<sub>z</sub>(1,1,1)</li> |
| * |
| * <li>f<sub>xy</sub>(0,0,0)</li> |
| * <li>... <em>(same order as above)</em></li> |
| * <li>f<sub>xy</sub>(1,1,1)</li> |
| * |
| * <li>f<sub>xz</sub>(0,0,0)</li> |
| * <li>... <em>(same order as above)</em></li> |
| * <li>f<sub>xz</sub>(1,1,1)</li> |
| * |
| * <li>f<sub>yz</sub>(0,0,0)</li> |
| * <li>... <em>(same order as above)</em></li> |
| * <li>f<sub>yz</sub>(1,1,1)</li> |
| * |
| * <li>f<sub>xyz</sub>(0,0,0)</li> |
| * <li>... <em>(same order as above)</em></li> |
| * <li>f<sub>xyz</sub>(1,1,1)</li> |
| * </ul> |
| * where the subscripts indicate the partial derivative with respect to |
| * the corresponding variable(s). |
| * |
| * @param beta List of function values and function partial derivatives values. |
| * @return the spline coefficients. |
| */ |
| private double[] 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]}. |
| */ |
| @Override |
| 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; |
| } |
| } |