| /* |
| * 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.statistics.distribution.ContinuousDistribution; |
| import org.apache.commons.statistics.distribution.UniformContinuousDistribution; |
| import org.apache.commons.math4.exception.DimensionMismatchException; |
| import org.apache.commons.math4.exception.MathIllegalArgumentException; |
| import org.apache.commons.rng.UniformRandomProvider; |
| import org.apache.commons.rng.simple.RandomSource; |
| import org.apache.commons.math4.util.FastMath; |
| import org.apache.commons.numbers.core.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 d3fdxdydz 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 UniformRandomProvider rng = RandomSource.create(RandomSource.WELL_19937_C, 1234568L); |
| final ContinuousDistribution.Sampler distX = new UniformContinuousDistribution(xValues[0], xValues[xValues.length - 1]).createSampler(rng); |
| final ContinuousDistribution.Sampler distY = new UniformContinuousDistribution(yValues[0], yValues[yValues.length - 1]).createSampler(rng); |
| final ContinuousDistribution.Sampler distZ = new UniformContinuousDistribution(zValues[0], zValues[zValues.length - 1]).createSampler(rng); |
| |
| 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() { |
| @Override |
| public double value(double x, double y, double z) { |
| return 2 * x - 3 * y - 4 * z + 5; |
| } |
| }; |
| |
| final TrivariateFunction dfdx = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return 2; |
| } |
| }; |
| |
| final TrivariateFunction dfdy = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return -3; |
| } |
| }; |
| |
| final TrivariateFunction dfdz = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return -4; |
| } |
| }; |
| |
| final TrivariateFunction zero = new TrivariateFunction() { |
| @Override |
| 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() { |
| @Override |
| 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() { |
| @Override |
| public double value(double x, double y, double z) { |
| return 4 * x + 5 * y + 6 * z; |
| } |
| }; |
| |
| final TrivariateFunction dfdy = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return -6 * y + 5 * x - 2 * z; |
| } |
| }; |
| |
| final TrivariateFunction dfdz = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return -8 * z + 6 * x - 2 * y; |
| } |
| }; |
| |
| final TrivariateFunction d2fdxdy = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return 5; |
| } |
| }; |
| |
| final TrivariateFunction d2fdxdz = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return 6; |
| } |
| }; |
| |
| final TrivariateFunction d2fdydz = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return -2; |
| } |
| }; |
| |
| final TrivariateFunction d3fdxdydz = new TrivariateFunction() { |
| @Override |
| 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() { |
| @Override |
| public double value(double x, double y, double z) { |
| return omega * z - kx * x - ky * y; |
| } |
| }; |
| |
| final TrivariateFunction f = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return a * FastMath.cos(arg.value(x, y, z)); |
| } |
| }; |
| |
| final TrivariateFunction dfdx = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return kx * a * FastMath.sin(arg.value(x, y, z)); |
| } |
| }; |
| |
| final TrivariateFunction dfdy = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return ky * a * FastMath.sin(arg.value(x, y, z)); |
| } |
| }; |
| |
| final TrivariateFunction dfdz = new TrivariateFunction() { |
| @Override |
| public double value(double x, double y, double z) { |
| return -omega * a * FastMath.sin(arg.value(x, y, z)); |
| } |
| }; |
| |
| final TrivariateFunction d2fdxdy = new TrivariateFunction() { |
| @Override |
| 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() { |
| @Override |
| 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() { |
| @Override |
| 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() { |
| @Override |
| 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); |
| } |
| } |