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Posted to commits@commons.apache.org by er...@apache.org on 2014/12/03 12:31:55 UTC
[2/3] [math] MATH-1173: Tricubic interpolation
MATH-1173: Tricubic interpolation
New class "TricubicInterpolatingFunction" to replace "TricubicSplineInterpolatingFunction".
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/fd7a4362
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/fd7a4362
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/fd7a4362
Branch: refs/heads/master
Commit: fd7a4362caf2cd69368a38f2f71ffe19706e341c
Parents: 17f52a2
Author: Gilles <er...@apache.org>
Authored: Wed Dec 3 12:25:09 2014 +0100
Committer: Gilles <er...@apache.org>
Committed: Wed Dec 3 12:25:09 2014 +0100
----------------------------------------------------------------------
.../TricubicInterpolatingFunction.java | 510 +++++++++++++++
.../TricubicInterpolatingFunctionTest.java | 631 +++++++++++++++++++
2 files changed, 1141 insertions(+)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-math/blob/fd7a4362/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatingFunction.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatingFunction.java b/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatingFunction.java
new file mode 100644
index 0000000..b527996
--- /dev/null
+++ b/src/main/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatingFunction.java
@@ -0,0 +1,510 @@
+/*
+ * 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.OutOfRangeException;
+import org.apache.commons.math3.exception.NonMonotonicSequenceException;
+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
+ * <quote>
+ * 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
+ * </quote>
+ *
+ * @since 2.2
+ * @deprecated in 3.4.
+ */
+@Deprecated
+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 pacthing 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.
+ */
+ 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.
+ */
+ public 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]}.
+ */
+ 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;
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/fd7a4362/src/test/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatingFunctionTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatingFunctionTest.java b/src/test/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatingFunctionTest.java
new file mode 100644
index 0000000..9760555
--- /dev/null
+++ b/src/test/java/org/apache/commons/math3/analysis/interpolation/TricubicInterpolatingFunctionTest.java
@@ -0,0 +1,631 @@
+/*
+ * 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.exception.DimensionMismatchException;
+import org.apache.commons.math3.exception.MathIllegalArgumentException;
+import org.apache.commons.math3.analysis.TrivariateFunction;
+import org.apache.commons.math3.distribution.UniformRealDistribution;
+import org.apache.commons.math3.random.RandomGenerator;
+import org.apache.commons.math3.random.Well19937c;
+import org.apache.commons.math3.util.FastMath;
+import org.apache.commons.math3.util.Precision;
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Test case for the bicubic function.
+ *
+ */
+public final class TricubicInterpolatingFunctionTest {
+ /**
+ * Test preconditions.
+ */
+ @Test
+ public void testPreconditions() {
+ double[] xval = new double[] {3, 4, 5, 6.5};
+ double[] yval = new double[] {-4, -3, -1, 2.5};
+ double[] zval = new double[] {-12, -8, -5.5, -3, 0, 2.5};
+ double[][][] fval = new double[xval.length][yval.length][zval.length];
+
+ @SuppressWarnings("unused")
+ TrivariateFunction tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, fval, fval, fval);
+
+ double[] wxval = new double[] {3, 2, 5, 6.5};
+ try {
+ tcf = new TricubicInterpolatingFunction(wxval, yval, zval,
+ fval, fval, fval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (MathIllegalArgumentException e) {
+ // Expected
+ }
+ double[] wyval = new double[] {-4, -1, -1, 2.5};
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, wyval, zval,
+ fval, fval, fval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (MathIllegalArgumentException e) {
+ // Expected
+ }
+ double[] wzval = new double[] {-12, -8, -9, -3, 0, 2.5};
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, wzval,
+ fval, fval, fval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (MathIllegalArgumentException e) {
+ // Expected
+ }
+ double[][][] wfval = new double[xval.length - 1][yval.length - 1][zval.length];
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ wfval, fval, fval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, wfval, fval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, wfval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, wfval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ wfval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, wfval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, fval, wfval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, fval, fval, wfval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ wfval = new double[xval.length][yval.length - 1][zval.length];
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ wfval, fval, fval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, wfval, fval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, wfval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, wfval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ wfval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, wfval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, fval, wfval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, fval, fval, wfval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ wfval = new double[xval.length][yval.length][zval.length - 1];
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ wfval, fval, fval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, wfval, fval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, wfval, fval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, wfval,
+ fval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ wfval, fval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, wfval, fval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, fval, wfval, fval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ try {
+ tcf = new TricubicInterpolatingFunction(xval, yval, zval,
+ fval, fval, fval, fval,
+ fval, fval, fval, wfval);
+ Assert.fail("an exception should have been thrown");
+ } catch (DimensionMismatchException e) {
+ // Expected
+ }
+ }
+
+ /**
+ * @param minimumX Lower bound of interpolation range along the x-coordinate.
+ * @param maximumX Higher bound of interpolation range along the x-coordinate.
+ * @param minimumY Lower bound of interpolation range along the y-coordinate.
+ * @param maximumY Higher bound of interpolation range along the y-coordinate.
+ * @param minimumZ Lower bound of interpolation range along the z-coordinate.
+ * @param maximumZ Higher bound of interpolation range along the z-coordinate.
+ * @param numberOfElements Number of data points (along each dimension).
+ * @param numberOfSamples Number of test points.
+ * @param f Function to test.
+ * @param dfdx Partial derivative w.r.t. x of the function to test.
+ * @param dfdy Partial derivative w.r.t. y of the function to test.
+ * @param dfdz Partial derivative w.r.t. z of the function to test.
+ * @param d2fdxdy Second partial cross-derivative w.r.t x and y of the function to test.
+ * @param d2fdxdz Second partial cross-derivative w.r.t x and z of the function to test.
+ * @param d2fdydz Second partial cross-derivative w.r.t y and z of the function to test.
+ * @param d3fdxdy Third partial cross-derivative w.r.t x, y and z of the function to test.
+ * @param meanRelativeTolerance Allowed average error (mean error on all interpolated values).
+ * @param maxRelativeTolerance Allowed error on each interpolated value.
+ * @param onDataMaxAbsoluteTolerance Allowed error on a data point.
+ */
+ private void testInterpolation(double minimumX,
+ double maximumX,
+ double minimumY,
+ double maximumY,
+ double minimumZ,
+ double maximumZ,
+ int numberOfElements,
+ int numberOfSamples,
+ TrivariateFunction f,
+ TrivariateFunction dfdx,
+ TrivariateFunction dfdy,
+ TrivariateFunction dfdz,
+ TrivariateFunction d2fdxdy,
+ TrivariateFunction d2fdxdz,
+ TrivariateFunction d2fdydz,
+ TrivariateFunction d3fdxdydz,
+ double meanRelativeTolerance,
+ double maxRelativeTolerance,
+ double onDataMaxAbsoluteTolerance,
+ boolean print) {
+ double expected;
+ double actual;
+ double currentX;
+ double currentY;
+ double currentZ;
+ final double deltaX = (maximumX - minimumX) / numberOfElements;
+ final double deltaY = (maximumY - minimumY) / numberOfElements;
+ final double deltaZ = (maximumZ - minimumZ) / numberOfElements;
+ final double[] xValues = new double[numberOfElements];
+ final double[] yValues = new double[numberOfElements];
+ final double[] zValues = new double[numberOfElements];
+ final double[][][] fValues = new double[numberOfElements][numberOfElements][numberOfElements];
+ final double[][][] dfdxValues = new double[numberOfElements][numberOfElements][numberOfElements];
+ final double[][][] dfdyValues = new double[numberOfElements][numberOfElements][numberOfElements];
+ final double[][][] dfdzValues = new double[numberOfElements][numberOfElements][numberOfElements];
+ final double[][][] d2fdxdyValues = new double[numberOfElements][numberOfElements][numberOfElements];
+ final double[][][] d2fdxdzValues = new double[numberOfElements][numberOfElements][numberOfElements];
+ final double[][][] d2fdydzValues = new double[numberOfElements][numberOfElements][numberOfElements];
+ final double[][][] d3fdxdydzValues = new double[numberOfElements][numberOfElements][numberOfElements];
+
+ for (int i = 0; i < numberOfElements; i++) {
+ xValues[i] = minimumX + deltaX * i;
+ final double x = xValues[i];
+ for (int j = 0; j < numberOfElements; j++) {
+ yValues[j] = minimumY + deltaY * j;
+ final double y = yValues[j];
+ for (int k = 0; k < numberOfElements; k++) {
+ zValues[k] = minimumZ + deltaZ * k;
+ final double z = zValues[k];
+ fValues[i][j][k] = f.value(x, y, z);
+ dfdxValues[i][j][k] = dfdx.value(x, y, z);
+ dfdyValues[i][j][k] = dfdy.value(x, y, z);
+ dfdzValues[i][j][k] = dfdz.value(x, y, z);
+ d2fdxdyValues[i][j][k] = d2fdxdy.value(x, y, z);
+ d2fdxdzValues[i][j][k] = d2fdxdz.value(x, y, z);
+ d2fdydzValues[i][j][k] = d2fdydz.value(x, y, z);
+ d3fdxdydzValues[i][j][k] = d3fdxdydz.value(x, y, z);
+ }
+ }
+ }
+
+ final TrivariateFunction interpolation
+ = new TricubicInterpolatingFunction(xValues,
+ yValues,
+ zValues,
+ fValues,
+ dfdxValues,
+ dfdyValues,
+ dfdzValues,
+ d2fdxdyValues,
+ d2fdxdzValues,
+ d2fdydzValues,
+ d3fdxdydzValues);
+
+ for (int i = 0; i < numberOfElements; i++) {
+ currentX = xValues[i];
+ for (int j = 0; j < numberOfElements; j++) {
+ currentY = yValues[j];
+ for (int k = 0; k < numberOfElements; k++) {
+ currentZ = zValues[k];
+ expected = f.value(currentX, currentY, currentZ);
+ actual = interpolation.value(currentX, currentY, currentZ);
+ Assert.assertTrue("On data point: " + expected + " != " + actual,
+ Precision.equals(expected, actual, onDataMaxAbsoluteTolerance));
+ }
+ }
+ }
+
+ final RandomGenerator rng = new Well19937c(1234567L);
+ final UniformRealDistribution distX = new UniformRealDistribution(rng, xValues[0], xValues[xValues.length - 1]);
+ final UniformRealDistribution distY = new UniformRealDistribution(rng, yValues[0], yValues[yValues.length - 1]);
+ final UniformRealDistribution distZ = new UniformRealDistribution(rng, zValues[0], zValues[zValues.length - 1]);
+
+ double sumError = 0;
+ for (int i = 0; i < numberOfSamples; i++) {
+ currentX = distX.sample();
+ currentY = distY.sample();
+ currentZ = distZ.sample();
+ expected = f.value(currentX, currentY, currentZ);
+
+ actual = interpolation.value(currentX, currentY, currentZ);
+ final double relativeError = FastMath.abs(actual - expected) / FastMath.max(FastMath.abs(actual), FastMath.abs(expected));
+ sumError += relativeError;
+
+ if (print) {
+ System.out.println(currentX + " " + currentY + " " + currentZ
+ + " " + actual
+ + " " + expected
+ + " " + (expected - actual));
+ }
+
+ Assert.assertEquals(0, relativeError, maxRelativeTolerance);
+ }
+
+ final double meanError = sumError / numberOfSamples;
+ Assert.assertEquals(0, meanError, meanRelativeTolerance);
+ }
+
+ /**
+ * Test for a plane.
+ * <p>
+ * f(x, y, z) = 2 x - 3 y - 4 z + 5
+ * </p>
+ */
+ @Test
+ public void testPlane() {
+ final TrivariateFunction f = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return 2 * x - 3 * y - 4 * z + 5;
+ }
+ };
+
+ final TrivariateFunction dfdx = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return 2;
+ }
+ };
+
+ final TrivariateFunction dfdy = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return -3;
+ }
+ };
+
+ final TrivariateFunction dfdz = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return -4;
+ }
+ };
+
+ final TrivariateFunction zero = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return 0;
+ }
+ };
+
+ testInterpolation(-10, 3,
+ 4.5, 6,
+ -150, -117,
+ 7,
+ 1000,
+ f,
+ dfdx,
+ dfdy,
+ dfdz,
+ zero,
+ zero,
+ zero,
+ zero,
+ 1e-12,
+ 1e-11,
+ 1e-10,
+ false);
+ }
+
+ /**
+ * Test for a quadric.
+ * <p>
+ * f(x, y, z) = 2 x<sup>2</sup> - 3 y<sup>2</sup> - 4 z<sup>2</sup> + 5 x y + 6 x z - 2 y z + 3
+ * </p>
+ */
+ @Test
+ public void testQuadric() {
+ final TrivariateFunction f = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return 2 * x * x - 3 * y * y - 4 * z * z + 5 * x * y + 6 * x * z - 2 * y * z + 3;
+ }
+ };
+
+ final TrivariateFunction dfdx = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return 4 * x + 5 * y + 6 * z;
+ }
+ };
+
+ final TrivariateFunction dfdy = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return -6 * y + 5 * x - 2 * z;
+ }
+ };
+
+ final TrivariateFunction dfdz = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return -8 * z + 6 * x - 2 * y;
+ }
+ };
+
+ final TrivariateFunction d2fdxdy = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return 5;
+ }
+ };
+
+ final TrivariateFunction d2fdxdz = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return 6;
+ }
+ };
+
+ final TrivariateFunction d2fdydz = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return -2;
+ }
+ };
+
+ final TrivariateFunction d3fdxdydz = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return 0;
+ }
+ };
+
+ testInterpolation(-10, 3,
+ 4.5, 6,
+ -150, -117,
+ 7,
+ 5000,
+ f,
+ dfdx,
+ dfdy,
+ dfdz,
+ d2fdxdy,
+ d2fdxdz,
+ d2fdydz,
+ d3fdxdydz,
+ 1e-12,
+ 1e-11,
+ 1e-8,
+ false);
+ }
+
+ /**
+ * Wave.
+ * <p>
+ * f(x, y, z) = a cos (ω z - k<sub>x</sub> x - k<sub>y</sub> y)
+ * </p>
+ * with a = 5, ω = 0.3, k<sub>x</sub> = 0.8, k<sub>y</sub> = 1.
+ */
+ @Test
+ public void testWave() {
+ final double a = 5;
+ final double omega = 0.3;
+ final double kx = 0.8;
+ final double ky = 1;
+
+ final TrivariateFunction arg = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return omega * z - kx * x - ky * y;
+ }
+ };
+
+ final TrivariateFunction f = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return a * FastMath.cos(arg.value(x, y, z));
+ }
+ };
+
+ final TrivariateFunction dfdx = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return kx * a * FastMath.sin(arg.value(x, y, z));
+ }
+ };
+
+ final TrivariateFunction dfdy = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return ky * a * FastMath.sin(arg.value(x, y, z));
+ }
+ };
+
+ final TrivariateFunction dfdz = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return -omega * a * FastMath.sin(arg.value(x, y, z));
+ }
+ };
+
+ final TrivariateFunction d2fdxdy = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return -ky * kx * a * FastMath.cos(arg.value(x, y, z));
+ }
+ };
+
+ final TrivariateFunction d2fdxdz = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return omega * kx * a * FastMath.cos(arg.value(x, y, z));
+ }
+ };
+
+ final TrivariateFunction d2fdydz = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return omega * ky * a * FastMath.cos(arg.value(x, y, z));
+ }
+ };
+
+ final TrivariateFunction d3fdxdydz = new TrivariateFunction() {
+ public double value(double x, double y, double z) {
+ return omega * ky * kx * a * FastMath.sin(arg.value(x, y, z));
+ }
+ };
+
+ testInterpolation(-10, 3,
+ 4.5, 6,
+ -150, -117,
+ 30,
+ 5000,
+ f,
+ dfdx,
+ dfdy,
+ dfdz,
+ d2fdxdy,
+ d2fdxdz,
+ d2fdydz,
+ d3fdxdydz,
+ 1e-3,
+ 1e-2,
+ 1e-12,
+ false);
+ }
+}