| /* |
| * 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.legacy.analysis.polynomials; |
| |
| import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException; |
| import org.junit.Assert; |
| import org.junit.Test; |
| |
| /** |
| * Test case for Lagrange form of polynomial function. |
| * <p> |
| * We use n+1 points to interpolate a polynomial of degree n. This should |
| * give us the exact same polynomial as result. Thus we can use a very |
| * small tolerance to account only for round-off errors. |
| * |
| */ |
| public final class PolynomialFunctionLagrangeFormTest { |
| |
| /** |
| * Test of polynomial for the linear function. |
| */ |
| @Test |
| public void testLinearFunction() { |
| PolynomialFunctionLagrangeForm p; |
| double[] c; |
| double z; |
| double expected; |
| double result; |
| double tolerance = 1E-12; |
| |
| // p(x) = 1.5x - 4 |
| double x[] = { 0.0, 3.0 }; |
| double y[] = { -4.0, 0.5 }; |
| p = new PolynomialFunctionLagrangeForm(x, y); |
| |
| 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()); |
| |
| c = p.getCoefficients(); |
| Assert.assertEquals(2, c.length); |
| Assert.assertEquals(-4.0, c[0], tolerance); |
| Assert.assertEquals(1.5, c[1], tolerance); |
| } |
| |
| /** |
| * Test of polynomial for the quadratic function. |
| */ |
| @Test |
| public void testQuadraticFunction() { |
| PolynomialFunctionLagrangeForm p; |
| double[] c; |
| double z; |
| double expected; |
| double result; |
| double tolerance = 1E-12; |
| |
| // p(x) = 2x^2 + 5x - 3 = (2x - 1)(x + 3) |
| double x[] = { 0.0, -1.0, 0.5 }; |
| double y[] = { -3.0, -6.0, 0.0 }; |
| p = new PolynomialFunctionLagrangeForm(x, y); |
| |
| 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()); |
| |
| c = p.getCoefficients(); |
| Assert.assertEquals(3, c.length); |
| Assert.assertEquals(-3.0, c[0], tolerance); |
| Assert.assertEquals(5.0, c[1], tolerance); |
| Assert.assertEquals(2.0, c[2], tolerance); |
| } |
| |
| /** |
| * Test of polynomial for the quintic function. |
| */ |
| @Test |
| public void testQuinticFunction() { |
| PolynomialFunctionLagrangeForm p; |
| double[] c; |
| double z; |
| double expected; |
| double result; |
| double tolerance = 1E-12; |
| |
| // p(x) = x^5 - x^4 - 7x^3 + x^2 + 6x = x(x^2 - 1)(x + 2)(x - 3) |
| double x[] = { 1.0, -1.0, 2.0, 3.0, -3.0, 0.5 }; |
| double y[] = { 0.0, 0.0, -24.0, 0.0, -144.0, 2.34375 }; |
| p = new PolynomialFunctionLagrangeForm(x, y); |
| |
| 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()); |
| |
| c = p.getCoefficients(); |
| Assert.assertEquals(6, c.length); |
| Assert.assertEquals(0.0, c[0], tolerance); |
| Assert.assertEquals(6.0, c[1], tolerance); |
| Assert.assertEquals(1.0, c[2], tolerance); |
| Assert.assertEquals(-7.0, c[3], tolerance); |
| Assert.assertEquals(-1.0, c[4], tolerance); |
| Assert.assertEquals(1.0, c[5], tolerance); |
| } |
| |
| /** |
| * Test of parameters for the polynomial. |
| */ |
| @Test |
| public void testParameters() { |
| |
| try { |
| // bad input array length |
| double x[] = { 1.0 }; |
| double y[] = { 2.0 }; |
| new PolynomialFunctionLagrangeForm(x, y); |
| Assert.fail("Expecting MathIllegalArgumentException - bad input array length"); |
| } catch (MathIllegalArgumentException ex) { |
| // expected |
| } |
| try { |
| // mismatch input arrays |
| double x[] = { 1.0, 2.0, 3.0, 4.0 }; |
| double y[] = { 0.0, -4.0, -24.0 }; |
| new PolynomialFunctionLagrangeForm(x, y); |
| Assert.fail("Expecting MathIllegalArgumentException - mismatch input arrays"); |
| } catch (MathIllegalArgumentException ex) { |
| // expected |
| } |
| } |
| } |