| /* |
| * 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.polynomials; |
| |
| import org.apache.commons.math4.analysis.differentiation.DerivativeStructure; |
| import org.apache.commons.math4.exception.MathIllegalArgumentException; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| |
| /** |
| * Test case for Newton form of polynomial function. |
| * <p> |
| * The small tolerance number is used only to account for round-off errors. |
| * |
| */ |
| public final class PolynomialFunctionNewtonFormTest { |
| |
| /** |
| * Test of polynomial for the linear function. |
| */ |
| @Test |
| public void testLinearFunction() { |
| PolynomialFunctionNewtonForm p; |
| double coefficients[], z, expected, result, tolerance = 1E-12; |
| |
| // p(x) = 1.5x - 4 = 2 + 1.5(x-4) |
| double a[] = { 2.0, 1.5 }; |
| double c[] = { 4.0 }; |
| p = new PolynomialFunctionNewtonForm(a, c); |
| |
| z = 2.0; expected = -1.0; result = p.value(z); |
| Assert.assertEquals(expected, result, tolerance); |
| |
| z = 4.5; expected = 2.75; result = p.value(z); |
| Assert.assertEquals(expected, result, tolerance); |
| |
| z = 6.0; expected = 5.0; result = p.value(z); |
| Assert.assertEquals(expected, result, tolerance); |
| |
| Assert.assertEquals(1, p.degree()); |
| |
| coefficients = p.getCoefficients(); |
| Assert.assertEquals(2, coefficients.length); |
| Assert.assertEquals(-4.0, coefficients[0], tolerance); |
| Assert.assertEquals(1.5, coefficients[1], tolerance); |
| } |
| |
| /** |
| * Test of polynomial for the quadratic function. |
| */ |
| @Test |
| public void testQuadraticFunction() { |
| PolynomialFunctionNewtonForm p; |
| double coefficients[], z, expected, result, tolerance = 1E-12; |
| |
| // p(x) = 2x^2 + 5x - 3 = 4 + 3(x-1) + 2(x-1)(x+2) |
| double a[] = { 4.0, 3.0, 2.0 }; |
| double c[] = { 1.0, -2.0 }; |
| p = new PolynomialFunctionNewtonForm(a, c); |
| |
| z = 1.0; expected = 4.0; result = p.value(z); |
| Assert.assertEquals(expected, result, tolerance); |
| |
| z = 2.5; expected = 22.0; result = p.value(z); |
| Assert.assertEquals(expected, result, tolerance); |
| |
| z = -2.0; expected = -5.0; result = p.value(z); |
| Assert.assertEquals(expected, result, tolerance); |
| |
| Assert.assertEquals(2, p.degree()); |
| |
| coefficients = p.getCoefficients(); |
| Assert.assertEquals(3, coefficients.length); |
| Assert.assertEquals(-3.0, coefficients[0], tolerance); |
| Assert.assertEquals(5.0, coefficients[1], tolerance); |
| Assert.assertEquals(2.0, coefficients[2], tolerance); |
| } |
| |
| /** |
| * Test of polynomial for the quintic function. |
| */ |
| @Test |
| public void testQuinticFunction() { |
| PolynomialFunctionNewtonForm p; |
| double coefficients[], z, expected, result, tolerance = 1E-12; |
| |
| // p(x) = x^5 - x^4 - 7x^3 + x^2 + 6x |
| // = 6x - 6x^2 -6x^2(x-1) + x^2(x-1)(x+1) + x^2(x-1)(x+1)(x-2) |
| double a[] = { 0.0, 6.0, -6.0, -6.0, 1.0, 1.0 }; |
| double c[] = { 0.0, 0.0, 1.0, -1.0, 2.0 }; |
| p = new PolynomialFunctionNewtonForm(a, c); |
| |
| z = 0.0; expected = 0.0; result = p.value(z); |
| Assert.assertEquals(expected, result, tolerance); |
| |
| z = -2.0; expected = 0.0; result = p.value(z); |
| Assert.assertEquals(expected, result, tolerance); |
| |
| z = 4.0; expected = 360.0; result = p.value(z); |
| Assert.assertEquals(expected, result, tolerance); |
| |
| Assert.assertEquals(5, p.degree()); |
| |
| coefficients = p.getCoefficients(); |
| Assert.assertEquals(6, coefficients.length); |
| Assert.assertEquals(0.0, coefficients[0], tolerance); |
| Assert.assertEquals(6.0, coefficients[1], tolerance); |
| Assert.assertEquals(1.0, coefficients[2], tolerance); |
| Assert.assertEquals(-7.0, coefficients[3], tolerance); |
| Assert.assertEquals(-1.0, coefficients[4], tolerance); |
| Assert.assertEquals(1.0, coefficients[5], tolerance); |
| } |
| |
| /** |
| * Test for derivatives. |
| */ |
| @Test |
| public void testDerivative() { |
| |
| // x^3 = 0 * [1] + 1 * [x] + 3 * [x(x-1)] + 1 * [x(x-1)(x-2)] |
| PolynomialFunctionNewtonForm p = |
| new PolynomialFunctionNewtonForm(new double[] { 0, 1, 3, 1 }, |
| new double[] { 0, 1, 2 }); |
| |
| double eps = 2.0e-14; |
| for (double t = 0.0; t < 10.0; t += 0.1) { |
| DerivativeStructure x = new DerivativeStructure(1, 4, 0, t); |
| DerivativeStructure y = p.value(x); |
| Assert.assertEquals(t * t * t, y.getValue(), eps * t * t * t); |
| Assert.assertEquals(3.0 * t * t, y.getPartialDerivative(1), eps * 3.0 * t * t); |
| Assert.assertEquals(6.0 * t, y.getPartialDerivative(2), eps * 6.0 * t); |
| Assert.assertEquals(6.0, y.getPartialDerivative(3), eps * 6.0); |
| Assert.assertEquals(0.0, y.getPartialDerivative(4), eps); |
| } |
| |
| } |
| |
| /** |
| * Test of parameters for the polynomial. |
| */ |
| @Test |
| public void testParameters() { |
| |
| try { |
| // bad input array length |
| double a[] = { 1.0 }; |
| double c[] = { 2.0 }; |
| new PolynomialFunctionNewtonForm(a, c); |
| Assert.fail("Expecting MathIllegalArgumentException - bad input array length"); |
| } catch (MathIllegalArgumentException ex) { |
| // expected |
| } |
| try { |
| // mismatch input arrays |
| double a[] = { 1.0, 2.0, 3.0, 4.0 }; |
| double c[] = { 4.0, 3.0, 2.0, 1.0 }; |
| new PolynomialFunctionNewtonForm(a, c); |
| Assert.fail("Expecting MathIllegalArgumentException - mismatch input arrays"); |
| } catch (MathIllegalArgumentException ex) { |
| // expected |
| } |
| } |
| } |