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diff --git a/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicSplineInterpolatingFunction.java b/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicSplineInterpolatingFunction.java
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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.analysis.interpolation;
+
+import org.apache.commons.math3.analysis.TrivariateFunction;
+import org.apache.commons.math3.exception.DimensionMismatchException;
+import org.apache.commons.math3.exception.NoDataException;
+import org.apache.commons.math3.exception.NonMonotonicSequenceException;
+import org.apache.commons.math3.exception.OutOfRangeException;
+import org.apache.commons.math3.util.MathArrays;
+
+/**
+ * Function that implements the
+ * <a href="http://en.wikipedia.org/wiki/Tricubic_interpolation">
+ * tricubic spline interpolation</a>, as proposed in
+ * <blockquote>
+ * Tricubic interpolation in three dimensions,
+ * F. Lekien and J. Marsden,
+ * <em>Int. J. Numer. Meth. Engng</em> 2005; <b>63</b>:455-471
+ * </blockquote>
+ *
+ * @since 2.2
+ * @deprecated To be removed in 4.0 (see MATH-1166).
+ */
+@Deprecated
+public class TricubicSplineInterpolatingFunction
+ 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 pacthing the whole data grid */
+ private final TricubicSplineFunction[][][] 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 TricubicSplineInterpolatingFunction(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 TricubicSplineFunction[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;
+ 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;
+ for (int k = 0; k < lastK; k++) {
+ final int kp1 = k + 1;
+
+ 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], dFdX[ip1][j][k],
+ dFdX[i][jp1][k], dFdX[ip1][jp1][k],
+ dFdX[i][j][kp1], dFdX[ip1][j][kp1],
+ dFdX[i][jp1][kp1], dFdX[ip1][jp1][kp1],
+
+ dFdY[i][j][k], dFdY[ip1][j][k],
+ dFdY[i][jp1][k], dFdY[ip1][jp1][k],
+ dFdY[i][j][kp1], dFdY[ip1][j][kp1],
+ dFdY[i][jp1][kp1], dFdY[ip1][jp1][kp1],
+
+ dFdZ[i][j][k], dFdZ[ip1][j][k],
+ dFdZ[i][jp1][k], dFdZ[ip1][jp1][k],
+ dFdZ[i][j][kp1], dFdZ[ip1][j][kp1],
+ dFdZ[i][jp1][kp1], dFdZ[ip1][jp1][kp1],
+
+ d2FdXdY[i][j][k], d2FdXdY[ip1][j][k],
+ d2FdXdY[i][jp1][k], d2FdXdY[ip1][jp1][k],
+ d2FdXdY[i][j][kp1], d2FdXdY[ip1][j][kp1],
+ d2FdXdY[i][jp1][kp1], d2FdXdY[ip1][jp1][kp1],
+
+ d2FdXdZ[i][j][k], d2FdXdZ[ip1][j][k],
+ d2FdXdZ[i][jp1][k], d2FdXdZ[ip1][jp1][k],
+ d2FdXdZ[i][j][kp1], d2FdXdZ[ip1][j][kp1],
+ d2FdXdZ[i][jp1][kp1], d2FdXdZ[ip1][jp1][kp1],
+
+ d2FdYdZ[i][j][k], d2FdYdZ[ip1][j][k],
+ d2FdYdZ[i][jp1][k], d2FdYdZ[ip1][jp1][k],
+ d2FdYdZ[i][j][kp1], d2FdYdZ[ip1][j][kp1],
+ d2FdYdZ[i][jp1][kp1], d2FdYdZ[ip1][jp1][kp1],
+
+ d3FdXdYdZ[i][j][k], d3FdXdYdZ[ip1][j][k],
+ d3FdXdYdZ[i][jp1][k], d3FdXdYdZ[ip1][jp1][k],
+ d3FdXdYdZ[i][j][kp1], d3FdXdYdZ[ip1][j][kp1],
+ d3FdXdYdZ[i][jp1][kp1], d3FdXdYdZ[ip1][jp1][kp1],
+ };
+
+ splines[i][j][k] = new TricubicSplineFunction(computeSplineCoefficients(beta));
+ }
+ }
+ }
+ }
+
+ /**
+ * {@inheritDoc}
+ *
+ * @throws OutOfRangeException if any of the variables is outside its interpolation range.
+ */
+ public double value(double x, double y, double z)
+ throws OutOfRangeException {
+ final int i = searchIndex(x, xval);
+ if (i == -1) {
+ throw new OutOfRangeException(x, xval[0], xval[xval.length - 1]);
+ }
+ final int j = searchIndex(y, yval);
+ if (j == -1) {
+ throw new OutOfRangeException(y, yval[0], yval[yval.length - 1]);
+ }
+ final int k = searchIndex(z, zval);
+ if (k == -1) {
+ throw new OutOfRangeException(z, zval[0], zval[zval.length - 1]);
+ }
+
+ final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);
+ final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);
+ final double zN = (z - zval[k]) / (zval[k + 1] - zval[k]);
+
+ return splines[i][j][k].value(xN, yN, zN);
+ }
+
+ /**
+ * @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[] computeSplineCoefficients(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 TricubicSplineFunction
+ 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.
+ */
+ TricubicSplineFunction(double[] aV) {
+ for (int i = 0; i < N; i++) {
+ for (int j = 0; j < N; j++) {
+ for (int k = 0; k < N; k++) {
+ a[i][j][k] = aV[i + N * (j + N * k)];
+ }
+ }
+ }
+ }
+
+ /**
+ * @param x x-coordinate of the interpolation point.
+ * @param y y-coordinate of the interpolation point.
+ * @param z z-coordinate of the interpolation point.
+ * @return the interpolated value.
+ * @throws OutOfRangeException if {@code x}, {@code y} or
+ * {@code z} are not in the interval {@code [0, 1]}.
+ */
+ public double value(double x, double y, double z)
+ throws OutOfRangeException {
+ if (x < 0 || x > 1) {
+ throw new OutOfRangeException(x, 0, 1);
+ }
+ if (y < 0 || y > 1) {
+ throw new OutOfRangeException(y, 0, 1);
+ }
+ if (z < 0 || z > 1) {
+ throw new OutOfRangeException(z, 0, 1);
+ }
+
+ final double x2 = x * x;
+ final double x3 = x2 * x;
+ final double[] pX = { 1, x, x2, x3 };
+
+ final double y2 = y * y;
+ final double y3 = y2 * y;
+ final double[] pY = { 1, y, y2, y3 };
+
+ final double z2 = z * z;
+ final double z3 = z2 * z;
+ final double[] pZ = { 1, z, z2, z3 };
+
+ double result = 0;
+ for (int i = 0; i < N; i++) {
+ for (int j = 0; j < N; j++) {
+ for (int k = 0; k < N; k++) {
+ result += a[i][j][k] * pX[i] * pY[j] * pZ[k];
+ }
+ }
+ }
+
+ return result;
+ }
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-13 22:02:07 +0000