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* Licensed to the Apache Software Foundation (ASF) under one or more
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* 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,
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* See the License for the specific language governing permissions and
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package org.apache.commons.math3.analysis.polynomials;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.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
}
}
}