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Java example source code file (BicubicSplineInterpolatingFunctionTest.java)
The BicubicSplineInterpolatingFunctionTest.java Java example source code/* * 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.exception.OutOfRangeException; import org.apache.commons.math3.analysis.BivariateFunction; import org.apache.commons.math3.distribution.UniformRealDistribution; import org.apache.commons.math3.random.RandomGenerator; import org.apache.commons.math3.random.Well19937c; import org.junit.Assert; import org.junit.Test; import org.junit.Ignore; /** * Test case for the bicubic function. * * @deprecated as of 3.4 replaced by * {@link org.apache.commons.math3.analysis.interpolation.PiecewiseBicubicSplineInterpolatingFunction} */ @Deprecated public final class BicubicSplineInterpolatingFunctionTest { /** * 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[xval.length][yval.length]; @SuppressWarnings("unused") BivariateFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, zval, zval, zval); double[] wxval = new double[] {3, 2, 5, 6.5}; try { bcf = new BicubicSplineInterpolatingFunction(wxval, yval, zval, zval, zval, zval); Assert.fail("an exception should have been thrown"); } catch (MathIllegalArgumentException e) { // Expected } double[] wyval = new double[] {-4, -1, -1, 2.5}; try { bcf = new BicubicSplineInterpolatingFunction(xval, wyval, zval, zval, zval, zval); Assert.fail("an exception should have been thrown"); } catch (MathIllegalArgumentException e) { // Expected } double[][] wzval = new double[xval.length][yval.length - 1]; try { bcf = new BicubicSplineInterpolatingFunction(xval, yval, wzval, zval, zval, zval); Assert.fail("an exception should have been thrown"); } catch (DimensionMismatchException e) { // Expected } try { bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, wzval, zval, zval); Assert.fail("an exception should have been thrown"); } catch (DimensionMismatchException e) { // Expected } try { bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, zval, wzval, zval); Assert.fail("an exception should have been thrown"); } catch (DimensionMismatchException e) { // Expected } try { bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, zval, zval, wzval); Assert.fail("an exception should have been thrown"); } catch (DimensionMismatchException e) { // Expected } wzval = new double[xval.length - 1][yval.length]; try { bcf = new BicubicSplineInterpolatingFunction(xval, yval, wzval, zval, zval, zval); Assert.fail("an exception should have been thrown"); } catch (DimensionMismatchException e) { // Expected } try { bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, wzval, zval, zval); Assert.fail("an exception should have been thrown"); } catch (DimensionMismatchException e) { // Expected } try { bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, zval, wzval, zval); Assert.fail("an exception should have been thrown"); } catch (DimensionMismatchException e) { // Expected } try { bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, zval, zval, wzval); Assert.fail("an exception should have been thrown"); } catch (DimensionMismatchException e) { // Expected } } /** * Test for a plane. * <p> * z = 2 x - 3 y + 5 */ @Ignore@Test public void testPlane() { double[] xval = new double[] {3, 4, 5, 6.5}; double[] yval = new double[] {-4, -3, -1, 2, 2.5}; // Function values BivariateFunction f = new BivariateFunction() { public double value(double x, double y) { return 2 * x - 3 * y + 5; } }; double[][] zval = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { zval[i][j] = f.value(xval[i], yval[j]); } } // Partial derivatives with respect to x double[][] dZdX = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdX[i][j] = 2; } } // Partial derivatives with respect to y double[][] dZdY = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdY[i][j] = -3; } } // Partial cross-derivatives double[][] dZdXdY = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdXdY[i][j] = 0; } } BivariateFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, dZdX, dZdY, dZdXdY); double x, y; double expected, result; x = 4; y = -3; expected = f.value(x, y); result = bcf.value(x, y); Assert.assertEquals("On sample point", expected, result, 1e-15); x = 4.5; y = -1.5; expected = f.value(x, y); result = bcf.value(x, y); Assert.assertEquals("Half-way between sample points (middle of the patch)", expected, result, 0.3); x = 3.5; y = -3.5; expected = f.value(x, y); result = bcf.value(x, y); Assert.assertEquals("Half-way between sample points (border of the patch)", expected, result, 0.3); } /** * Test for a paraboloid. * <p> * z = 2 x<sup>2 - 3 y2 + 4 x y - 5 */ @Ignore@Test public void testParaboloid() { double[] xval = new double[] {3, 4, 5, 6.5}; double[] yval = new double[] {-4, -3, -1, 2, 2.5}; // Function values BivariateFunction f = new BivariateFunction() { public double value(double x, double y) { return 2 * x * x - 3 * y * y + 4 * x * y - 5; } }; double[][] zval = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { zval[i][j] = f.value(xval[i], yval[j]); } } // Partial derivatives with respect to x double[][] dZdX = new double[xval.length][yval.length]; BivariateFunction dfdX = new BivariateFunction() { public double value(double x, double y) { return 4 * (x + y); } }; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdX[i][j] = dfdX.value(xval[i], yval[j]); } } // Partial derivatives with respect to y double[][] dZdY = new double[xval.length][yval.length]; BivariateFunction dfdY = new BivariateFunction() { public double value(double x, double y) { return 4 * x - 6 * y; } }; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdY[i][j] = dfdY.value(xval[i], yval[j]); } } // Partial cross-derivatives double[][] dZdXdY = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdXdY[i][j] = 4; } } BivariateFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, dZdX, dZdY, dZdXdY); double x, y; double expected, result; x = 4; y = -3; expected = f.value(x, y); result = bcf.value(x, y); Assert.assertEquals("On sample point", expected, result, 1e-15); x = 4.5; y = -1.5; expected = f.value(x, y); result = bcf.value(x, y); Assert.assertEquals("Half-way between sample points (middle of the patch)", expected, result, 2); x = 3.5; y = -3.5; expected = f.value(x, y); result = bcf.value(x, y); Assert.assertEquals("Half-way between sample points (border of the patch)", expected, result, 2); } /** * Test for partial derivatives of {@link BicubicSplineFunction}. * <p> * f(x, y) = ?<sub>i?j (i+1) (j+2) xi yj */ @Ignore@Test public void testSplinePartialDerivatives() { final int N = 4; final double[] coeff = new double[16]; for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { coeff[i + N * j] = (i + 1) * (j + 2); } } final BicubicSplineFunction f = new BicubicSplineFunction(coeff); BivariateFunction derivative; final double x = 0.435; final double y = 0.776; final double tol = 1e-13; derivative = new BivariateFunction() { public double value(double x, double y) { final double x2 = x * x; final double y2 = y * y; final double y3 = y2 * y; final double yFactor = 2 + 3 * y + 4 * y2 + 5 * y3; return yFactor * (2 + 6 * x + 12 * x2); } }; Assert.assertEquals("dFdX", derivative.value(x, y), f.partialDerivativeX().value(x, y), tol); derivative = new BivariateFunction() { public double value(double x, double y) { final double x2 = x * x; final double x3 = x2 * x; final double y2 = y * y; final double xFactor = 1 + 2 * x + 3 * x2 + 4 * x3; return xFactor * (3 + 8 * y + 15 * y2); } }; Assert.assertEquals("dFdY", derivative.value(x, y), f.partialDerivativeY().value(x, y), tol); derivative = new BivariateFunction() { public double value(double x, double y) { final double y2 = y * y; final double y3 = y2 * y; final double yFactor = 2 + 3 * y + 4 * y2 + 5 * y3; return yFactor * (6 + 24 * x); } }; Assert.assertEquals("d2FdX2", derivative.value(x, y), f.partialDerivativeXX().value(x, y), tol); derivative = new BivariateFunction() { public double value(double x, double y) { final double x2 = x * x; final double x3 = x2 * x; final double xFactor = 1 + 2 * x + 3 * x2 + 4 * x3; return xFactor * (8 + 30 * y); } }; Assert.assertEquals("d2FdY2", derivative.value(x, y), f.partialDerivativeYY().value(x, y), tol); derivative = new BivariateFunction() { public double value(double x, double y) { final double x2 = x * x; final double y2 = y * y; final double yFactor = 3 + 8 * y + 15 * y2; return yFactor * (2 + 6 * x + 12 * x2); } }; Assert.assertEquals("d2FdXdY", derivative.value(x, y), f.partialDerivativeXY().value(x, y), tol); } /** * Test that the partial derivatives computed from a * {@link BicubicSplineInterpolatingFunction} match the input data. * <p> * f(x, y) = 5 * - 3 x + 2 y * - x y + 2 x<sup>2 - 3 y2 * + 4 x<sup>2 y - x y2 - 3 x3 + y3 */ @Ignore@Test public void testMatchingPartialDerivatives() { final int sz = 21; double[] val = new double[sz]; // Coordinate values final double delta = 1d / (sz - 1); for (int i = 0; i < sz; i++) { val[i] = i * delta; } // Function values BivariateFunction f = new BivariateFunction() { public double value(double x, double y) { final double x2 = x * x; final double x3 = x2 * x; final double y2 = y * y; final double y3 = y2 * y; return 5 - 3 * x + 2 * y - x * y + 2 * x2 - 3 * y2 + 4 * x2 * y - x * y2 - 3 * x3 + y3; } }; double[][] fval = new double[sz][sz]; for (int i = 0; i < sz; i++) { for (int j = 0; j < sz; j++) { fval[i][j] = f.value(val[i], val[j]); } } // Partial derivatives with respect to x double[][] dFdX = new double[sz][sz]; BivariateFunction dfdX = new BivariateFunction() { public double value(double x, double y) { final double x2 = x * x; final double y2 = y * y; return - 3 - y + 4 * x + 8 * x * y - y2 - 9 * x2; } }; for (int i = 0; i < sz; i++) { for (int j = 0; j < sz; j++) { dFdX[i][j] = dfdX.value(val[i], val[j]); } } // Partial derivatives with respect to y double[][] dFdY = new double[sz][sz]; BivariateFunction dfdY = new BivariateFunction() { public double value(double x, double y) { final double x2 = x * x; final double y2 = y * y; return 2 - x - 6 * y + 4 * x2 - 2 * x * y + 3 * y2; } }; for (int i = 0; i < sz; i++) { for (int j = 0; j < sz; j++) { dFdY[i][j] = dfdY.value(val[i], val[j]); } } // Partial cross-derivatives double[][] d2FdXdY = new double[sz][sz]; BivariateFunction d2fdXdY = new BivariateFunction() { public double value(double x, double y) { return -1 + 8 * x - 2 * y; } }; for (int i = 0; i < sz; i++) { for (int j = 0; j < sz; j++) { d2FdXdY[i][j] = d2fdXdY.value(val[i], val[j]); } } BicubicSplineInterpolatingFunction bcf = new BicubicSplineInterpolatingFunction(val, val, fval, dFdX, dFdY, d2FdXdY); double x, y; double expected, result; final double tol = 1e-12; for (int i = 0; i < sz; i++) { x = val[i]; for (int j = 0; j < sz; j++) { y = val[j]; expected = dfdX.value(x, y); result = bcf.partialDerivativeX(x, y); Assert.assertEquals(x + " " + y + " dFdX", expected, result, tol); expected = dfdY.value(x, y); result = bcf.partialDerivativeY(x, y); Assert.assertEquals(x + " " + y + " dFdY", expected, result, tol); expected = d2fdXdY.value(x, y); result = bcf.partialDerivativeXY(x, y); Assert.assertEquals(x + " " + y + " d2FdXdY", expected, result, tol); } } } /** * Interpolating a plane. * <p> * z = 2 x - 3 y + 5 */ @Test public void testInterpolation1() { final int sz = 21; double[] xval = new double[sz]; double[] yval = new double[sz]; // Coordinate values final double delta = 1d / (sz - 1); for (int i = 0; i < sz; i++) { xval[i] = -1 + 15 * i * delta; yval[i] = -20 + 30 * i * delta; } // Function values BivariateFunction f = new BivariateFunction() { public double value(double x, double y) { return 2 * x - 3 * y + 5; } }; double[][] zval = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { zval[i][j] = f.value(xval[i], yval[j]); } } // Partial derivatives with respect to x double[][] dZdX = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdX[i][j] = 2; } } // Partial derivatives with respect to y double[][] dZdY = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdY[i][j] = -3; } } // Partial cross-derivatives double[][] dZdXdY = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdXdY[i][j] = 0; } } final BivariateFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, dZdX, dZdY, dZdXdY); double x, y; final RandomGenerator rng = new Well19937c(1234567L); // "tol" depends on the seed. final UniformRealDistribution distX = new UniformRealDistribution(rng, xval[0], xval[xval.length - 1]); final UniformRealDistribution distY = new UniformRealDistribution(rng, yval[0], yval[yval.length - 1]); final int numSamples = 50; final double tol = 6; for (int i = 0; i < numSamples; i++) { x = distX.sample(); for (int j = 0; j < numSamples; j++) { y = distY.sample(); // System.out.println(x + " " + y + " " + f.value(x, y) + " " + bcf.value(x, y)); Assert.assertEquals(f.value(x, y), bcf.value(x, y), tol); } // System.out.println(); } } /** * Interpolating a paraboloid. * <p> * z = 2 x<sup>2 - 3 y2 + 4 x y - 5 */ @Test public void testInterpolation2() { final int sz = 21; double[] xval = new double[sz]; double[] yval = new double[sz]; // Coordinate values final double delta = 1d / (sz - 1); for (int i = 0; i < sz; i++) { xval[i] = -1 + 15 * i * delta; yval[i] = -20 + 30 * i * delta; } // Function values BivariateFunction f = new BivariateFunction() { public double value(double x, double y) { return 2 * x * x - 3 * y * y + 4 * x * y - 5; } }; double[][] zval = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { zval[i][j] = f.value(xval[i], yval[j]); } } // Partial derivatives with respect to x double[][] dZdX = new double[xval.length][yval.length]; BivariateFunction dfdX = new BivariateFunction() { public double value(double x, double y) { return 4 * (x + y); } }; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdX[i][j] = dfdX.value(xval[i], yval[j]); } } // Partial derivatives with respect to y double[][] dZdY = new double[xval.length][yval.length]; BivariateFunction dfdY = new BivariateFunction() { public double value(double x, double y) { return 4 * x - 6 * y; } }; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdY[i][j] = dfdY.value(xval[i], yval[j]); } } // Partial cross-derivatives double[][] dZdXdY = new double[xval.length][yval.length]; for (int i = 0; i < xval.length; i++) { for (int j = 0; j < yval.length; j++) { dZdXdY[i][j] = 4; } } BivariateFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, zval, dZdX, dZdY, dZdXdY); double x, y; final RandomGenerator rng = new Well19937c(1234567L); // "tol" depends on the seed. final UniformRealDistribution distX = new UniformRealDistribution(rng, xval[0], xval[xval.length - 1]); final UniformRealDistribution distY = new UniformRealDistribution(rng, yval[0], yval[yval.length - 1]); final double tol = 224; for (int i = 0; i < sz; i++) { x = distX.sample(); for (int j = 0; j < sz; j++) { y = distY.sample(); // System.out.println(x + " " + y + " " + f.value(x, y) + " " + bcf.value(x, y)); Assert.assertEquals(f.value(x, y), bcf.value(x, y), tol); } // System.out.println(); } } @Test public void testIsValidPoint() { final double xMin = -12; final double xMax = 34; final double yMin = 5; final double yMax = 67; final double[] xval = new double[] { xMin, xMax }; final double[] yval = new double[] { yMin, yMax }; final double[][] f = new double[][] { { 1, 2 }, { 3, 4 } }; final double[][] dFdX = f; final double[][] dFdY = f; final double[][] dFdXdY = f; final BicubicSplineInterpolatingFunction bcf = new BicubicSplineInterpolatingFunction(xval, yval, f, dFdX, dFdY, dFdXdY); double x, y; x = xMin; y = yMin; Assert.assertTrue(bcf.isValidPoint(x, y)); // Ensure that no exception is thrown. bcf.value(x, y); x = xMax; y = yMax; Assert.assertTrue(bcf.isValidPoint(x, y)); // Ensure that no exception is thrown. bcf.value(x, y); final double xRange = xMax - xMin; final double yRange = yMax - yMin; x = xMin + xRange / 3.4; y = yMin + yRange / 1.2; Assert.assertTrue(bcf.isValidPoint(x, y)); // Ensure that no exception is thrown. bcf.value(x, y); final double small = 1e-8; x = xMin - small; y = yMax; Assert.assertFalse(bcf.isValidPoint(x, y)); // Ensure that an exception would have been thrown. try { bcf.value(x, y); Assert.fail("OutOfRangeException expected"); } catch (OutOfRangeException expected) {} x = xMin; y = yMax + small; Assert.assertFalse(bcf.isValidPoint(x, y)); // Ensure that an exception would have been thrown. try { bcf.value(x, y); Assert.fail("OutOfRangeException expected"); } catch (OutOfRangeException expected) {} } } Other Java examples (source code examples)Here is a short list of links related to this Java BicubicSplineInterpolatingFunctionTest.java source code file: |
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