/*
* 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.util.FastMath;
import org.apache.commons.math3.analysis.TrivariateFunction;
import org.junit.Assert;
import org.junit.Test;
/**
* Test case for the bicubic function.
*
*/
public final class TricubicSplineInterpolatingFunctionTest {
/**
* 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 TricubicSplineInterpolatingFunction(xval, yval, zval,
fval, fval, fval, fval,
fval, fval, fval, fval);
double[] wxval = new double[] {3, 2, 5, 6.5};
try {
tcf = new TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(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 TricubicSplineInterpolatingFunction(xval, yval, zval,
fval, fval, fval, fval,
fval, fval, fval, wfval);
Assert.fail("an exception should have been thrown");
} catch (DimensionMismatchException e) {
// Expected
}
}
/**
* Test for a plane.
* <p>
* f(x, y, z) = 2 x - 3 y - 4 z + 5
* </p>
*/
@Test
public void testPlane() {
double[] xval = new double[] {3, 4, 5, 6.5};
double[] yval = new double[] {-4, -3, -1, 2, 2.5};
double[] zval = new double[] {-12, -8, -5.5, -3, 0, 2.5};
// Function values
TrivariateFunction f = new TrivariateFunction() {
public double value(double x, double y, double z) {
return 2 * x - 3 * y - 4 * z + 5;
}
};
double[][][] fval = new double[xval.length][yval.length][zval.length];
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
fval[i][j][k] = f.value(xval[i], yval[j], zval[k]);
}
}
}
// Partial derivatives with respect to x
double[][][] dFdX = new double[xval.length][yval.length][zval.length];
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
dFdX[i][j][k] = 2;
}
}
}
// Partial derivatives with respect to y
double[][][] dFdY = new double[xval.length][yval.length][zval.length];
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
dFdY[i][j][k] = -3;
}
}
}
// Partial derivatives with respect to z
double[][][] dFdZ = new double[xval.length][yval.length][zval.length];
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
dFdZ[i][j][k] = -4;
}
}
}
// Partial cross-derivatives
double[][][] d2FdXdY = new double[xval.length][yval.length][zval.length];
double[][][] d2FdXdZ = new double[xval.length][yval.length][zval.length];
double[][][] d2FdYdZ = new double[xval.length][yval.length][zval.length];
double[][][] d3FdXdYdZ = new double[xval.length][yval.length][zval.length];
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
d2FdXdY[i][j][k] = 0;
d2FdXdZ[i][j][k] = 0;
d2FdYdZ[i][j][k] = 0;
d3FdXdYdZ[i][j][k] = 0;
}
}
}
TrivariateFunction tcf = new TricubicSplineInterpolatingFunction(xval, yval, zval,
fval, dFdX, dFdY, dFdZ,
d2FdXdY, d2FdXdZ, d2FdYdZ,
d3FdXdYdZ);
double x, y, z;
double expected, result;
x = 4;
y = -3;
z = 0;
expected = f.value(x, y, z);
result = tcf.value(x, y, z);
Assert.assertEquals("On sample point",
expected, result, 1e-15);
x = 4.5;
y = -1.5;
z = -4.25;
expected = f.value(x, y, z);
result = tcf.value(x, y, z);
Assert.assertEquals("Half-way between sample points (middle of the patch)",
expected, result, 0.3);
x = 3.5;
y = -3.5;
z = -10;
expected = f.value(x, y, z);
result = tcf.value(x, y, z);
Assert.assertEquals("Half-way between sample points (border of the patch)",
expected, result, 0.3);
}
/**
* Sine wave.
* <p>
* f(x, y, z) = a cos [ω z - k<sub>y</sub> x - k<sub>y</sub> y]
* </p>
* with A = 0.2, ω = 0.5, k<sub>x</sub> = 2, k<sub>y</sub> = 1.
*/
@Test
public void testWave() {
double[] xval = new double[] {3, 4, 5, 6.5};
double[] yval = new double[] {-4, -3, -1, 2, 2.5};
double[] zval = new double[] {-12, -8, -5.5, -3, 0, 4};
final double a = 0.2;
final double omega = 0.5;
final double kx = 2;
final double ky = 1;
// Function values
TrivariateFunction f = new TrivariateFunction() {
public double value(double x, double y, double z) {
return a * FastMath.cos(omega * z - kx * x - ky * y);
}
};
double[][][] fval = new double[xval.length][yval.length][zval.length];
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
fval[i][j][k] = f.value(xval[i], yval[j], zval[k]);
}
}
}
// Partial derivatives with respect to x
double[][][] dFdX = new double[xval.length][yval.length][zval.length];
TrivariateFunction dFdX_f = new TrivariateFunction() {
public double value(double x, double y, double z) {
return a * FastMath.sin(omega * z - kx * x - ky * y) * kx;
}
};
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
dFdX[i][j][k] = dFdX_f.value(xval[i], yval[j], zval[k]);
}
}
}
// Partial derivatives with respect to y
double[][][] dFdY = new double[xval.length][yval.length][zval.length];
TrivariateFunction dFdY_f = new TrivariateFunction() {
public double value(double x, double y, double z) {
return a * FastMath.sin(omega * z - kx * x - ky * y) * ky;
}
};
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
dFdY[i][j][k] = dFdY_f.value(xval[i], yval[j], zval[k]);
}
}
}
// Partial derivatives with respect to z
double[][][] dFdZ = new double[xval.length][yval.length][zval.length];
TrivariateFunction dFdZ_f = new TrivariateFunction() {
public double value(double x, double y, double z) {
return -a * FastMath.sin(omega * z - kx * x - ky * y) * omega;
}
};
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
dFdZ[i][j][k] = dFdZ_f.value(xval[i], yval[j], zval[k]);
}
}
}
// Partial second derivatives w.r.t. (x, y)
double[][][] d2FdXdY = new double[xval.length][yval.length][zval.length];
TrivariateFunction d2FdXdY_f = new TrivariateFunction() {
public double value(double x, double y, double z) {
return -a * FastMath.cos(omega * z - kx * x - ky * y) * kx * ky;
}
};
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
d2FdXdY[i][j][k] = d2FdXdY_f.value(xval[i], yval[j], zval[k]);
}
}
}
// Partial second derivatives w.r.t. (x, z)
double[][][] d2FdXdZ = new double[xval.length][yval.length][zval.length];
TrivariateFunction d2FdXdZ_f = new TrivariateFunction() {
public double value(double x, double y, double z) {
return a * FastMath.cos(omega * z - kx * x - ky * y) * kx * omega;
}
};
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
d2FdXdZ[i][j][k] = d2FdXdZ_f.value(xval[i], yval[j], zval[k]);
}
}
}
// Partial second derivatives w.r.t. (y, z)
double[][][] d2FdYdZ = new double[xval.length][yval.length][zval.length];
TrivariateFunction d2FdYdZ_f = new TrivariateFunction() {
public double value(double x, double y, double z) {
return a * FastMath.cos(omega * z - kx * x - ky * y) * ky * omega;
}
};
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
d2FdYdZ[i][j][k] = d2FdYdZ_f.value(xval[i], yval[j], zval[k]);
}
}
}
// Partial third derivatives
double[][][] d3FdXdYdZ = new double[xval.length][yval.length][zval.length];
TrivariateFunction d3FdXdYdZ_f = new TrivariateFunction() {
public double value(double x, double y, double z) {
return a * FastMath.sin(omega * z - kx * x - ky * y) * kx * ky * omega;
}
};
for (int i = 0; i < xval.length; i++) {
for (int j = 0; j < yval.length; j++) {
for (int k = 0; k < zval.length; k++) {
d3FdXdYdZ[i][j][k] = d3FdXdYdZ_f.value(xval[i], yval[j], zval[k]);
}
}
}
TrivariateFunction tcf = new TricubicSplineInterpolatingFunction(xval, yval, zval,
fval, dFdX, dFdY, dFdZ,
d2FdXdY, d2FdXdZ, d2FdYdZ,
d3FdXdYdZ);
double x, y, z;
double expected, result;
x = 4;
y = -3;
z = 0;
expected = f.value(x, y, z);
result = tcf.value(x, y, z);
Assert.assertEquals("On sample point",
expected, result, 1e-14);
x = 4.5;
y = -1.5;
z = -4.25;
expected = f.value(x, y, z);
result = tcf.value(x, y, z);
Assert.assertEquals("Half-way between sample points (middle of the patch)",
expected, result, 0.1);
x = 3.5;
y = -3.5;
z = -10;
expected = f.value(x, y, z);
result = tcf.value(x, y, z);
Assert.assertEquals("Half-way between sample points (border of the patch)",
expected, result, 0.1);
}
}