/*
* 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.TestUtils;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Tests the PolynomialFunction implementation of a UnivariateFunction.
*
*/
public final class PolynomialFunctionTest {
/** Error tolerance for tests */
protected double tolerance = 1e-12;
/**
* tests the value of a constant polynomial.
*
* <p>value of this is 2.5 everywhere.</p>
*/
@Test
public void testConstants() {
double[] c = { 2.5 };
PolynomialFunction f = new PolynomialFunction(c);
// verify that we are equal to c[0] at several (nonsymmetric) places
Assert.assertEquals(f.value(0), c[0], tolerance);
Assert.assertEquals(f.value(-1), c[0], tolerance);
Assert.assertEquals(f.value(-123.5), c[0], tolerance);
Assert.assertEquals(f.value(3), c[0], tolerance);
Assert.assertEquals(f.value(456.89), c[0], tolerance);
Assert.assertEquals(f.degree(), 0);
Assert.assertEquals(f.polynomialDerivative().value(0), 0, tolerance);
Assert.assertEquals(f.polynomialDerivative().polynomialDerivative().value(0), 0, tolerance);
}
/**
* tests the value of a linear polynomial.
*
* <p>This will test the function f(x) = 3*x - 1.5</p>
* <p>This will have the values
* <tt>f(0) = -1.5, f(-1) = -4.5, f(-2.5) = -9,
* f(0.5) = 0, f(1.5) = 3</tt> and {@code f(3) = 7.5}
* </p>
*/
@Test
public void testLinear() {
double[] c = { -1.5, 3 };
PolynomialFunction f = new PolynomialFunction(c);
// verify that we are equal to c[0] when x=0
Assert.assertEquals(f.value(0), c[0], tolerance);
// now check a few other places
Assert.assertEquals(-4.5, f.value(-1), tolerance);
Assert.assertEquals(-9, f.value(-2.5), tolerance);
Assert.assertEquals(0, f.value(0.5), tolerance);
Assert.assertEquals(3, f.value(1.5), tolerance);
Assert.assertEquals(7.5, f.value(3), tolerance);
Assert.assertEquals(f.degree(), 1);
Assert.assertEquals(f.polynomialDerivative().polynomialDerivative().value(0), 0, tolerance);
}
/**
* Tests a second order polynomial.
* <p> This will test the function f(x) = 2x^2 - 3x -2 = (2x+1)(x-2)</p>
*/
@Test
public void testQuadratic() {
double[] c = { -2, -3, 2 };
PolynomialFunction f = new PolynomialFunction(c);
// verify that we are equal to c[0] when x=0
Assert.assertEquals(f.value(0), c[0], tolerance);
// now check a few other places
Assert.assertEquals(0, f.value(-0.5), tolerance);
Assert.assertEquals(0, f.value(2), tolerance);
Assert.assertEquals(-2, f.value(1.5), tolerance);
Assert.assertEquals(7, f.value(-1.5), tolerance);
Assert.assertEquals(265.5312, f.value(12.34), tolerance);
}
/**
* This will test the quintic function
* f(x) = x^2(x-5)(x+3)(x-1) = x^5 - 3x^4 -13x^3 + 15x^2</p>
*/
@Test
public void testQuintic() {
double[] c = { 0, 0, 15, -13, -3, 1 };
PolynomialFunction f = new PolynomialFunction(c);
// verify that we are equal to c[0] when x=0
Assert.assertEquals(f.value(0), c[0], tolerance);
// now check a few other places
Assert.assertEquals(0, f.value(5), tolerance);
Assert.assertEquals(0, f.value(1), tolerance);
Assert.assertEquals(0, f.value(-3), tolerance);
Assert.assertEquals(54.84375, f.value(-1.5), tolerance);
Assert.assertEquals(-8.06637, f.value(1.3), tolerance);
Assert.assertEquals(f.degree(), 5);
}
/**
* tests the firstDerivative function by comparison
*
* <p>This will test the functions
* {@code f(x) = x^3 - 2x^2 + 6x + 3, g(x) = 3x^2 - 4x + 6}
* and {@code h(x) = 6x - 4}
*/
@Test
public void testfirstDerivativeComparison() {
double[] f_coeff = { 3, 6, -2, 1 };
double[] g_coeff = { 6, -4, 3 };
double[] h_coeff = { -4, 6 };
PolynomialFunction f = new PolynomialFunction(f_coeff);
PolynomialFunction g = new PolynomialFunction(g_coeff);
PolynomialFunction h = new PolynomialFunction(h_coeff);
// compare f' = g
Assert.assertEquals(f.polynomialDerivative().value(0), g.value(0), tolerance);
Assert.assertEquals(f.polynomialDerivative().value(1), g.value(1), tolerance);
Assert.assertEquals(f.polynomialDerivative().value(100), g.value(100), tolerance);
Assert.assertEquals(f.polynomialDerivative().value(4.1), g.value(4.1), tolerance);
Assert.assertEquals(f.polynomialDerivative().value(-3.25), g.value(-3.25), tolerance);
// compare g' = h
Assert.assertEquals(g.polynomialDerivative().value(FastMath.PI), h.value(FastMath.PI), tolerance);
Assert.assertEquals(g.polynomialDerivative().value(FastMath.E), h.value(FastMath.E), tolerance);
}
@Test
public void testString() {
PolynomialFunction p = new PolynomialFunction(new double[] { -5, 3, 1 });
checkPolynomial(p, "-5 + 3 x + x^2");
checkPolynomial(new PolynomialFunction(new double[] { 0, -2, 3 }),
"-2 x + 3 x^2");
checkPolynomial(new PolynomialFunction(new double[] { 1, -2, 3 }),
"1 - 2 x + 3 x^2");
checkPolynomial(new PolynomialFunction(new double[] { 0, 2, 3 }),
"2 x + 3 x^2");
checkPolynomial(new PolynomialFunction(new double[] { 1, 2, 3 }),
"1 + 2 x + 3 x^2");
checkPolynomial(new PolynomialFunction(new double[] { 1, 0, 3 }),
"1 + 3 x^2");
checkPolynomial(new PolynomialFunction(new double[] { 0 }),
"0");
}
@Test
public void testAddition() {
PolynomialFunction p1 = new PolynomialFunction(new double[] { -2, 1 });
PolynomialFunction p2 = new PolynomialFunction(new double[] { 2, -1, 0 });
checkNullPolynomial(p1.add(p2));
p2 = p1.add(p1);
checkPolynomial(p2, "-4 + 2 x");
p1 = new PolynomialFunction(new double[] { 1, -4, 2 });
p2 = new PolynomialFunction(new double[] { -1, 3, -2 });
p1 = p1.add(p2);
Assert.assertEquals(1, p1.degree());
checkPolynomial(p1, "-x");
}
@Test
public void testSubtraction() {
PolynomialFunction p1 = new PolynomialFunction(new double[] { -2, 1 });
checkNullPolynomial(p1.subtract(p1));
PolynomialFunction p2 = new PolynomialFunction(new double[] { -2, 6 });
p2 = p2.subtract(p1);
checkPolynomial(p2, "5 x");
p1 = new PolynomialFunction(new double[] { 1, -4, 2 });
p2 = new PolynomialFunction(new double[] { -1, 3, 2 });
p1 = p1.subtract(p2);
Assert.assertEquals(1, p1.degree());
checkPolynomial(p1, "2 - 7 x");
}
@Test
public void testMultiplication() {
PolynomialFunction p1 = new PolynomialFunction(new double[] { -3, 2 });
PolynomialFunction p2 = new PolynomialFunction(new double[] { 3, 2, 1 });
checkPolynomial(p1.multiply(p2), "-9 + x^2 + 2 x^3");
p1 = new PolynomialFunction(new double[] { 0, 1 });
p2 = p1;
for (int i = 2; i < 10; ++i) {
p2 = p2.multiply(p1);
checkPolynomial(p2, "x^" + i);
}
}
@Test
public void testSerial() {
PolynomialFunction p2 = new PolynomialFunction(new double[] { 3, 2, 1 });
Assert.assertEquals(p2, TestUtils.serializeAndRecover(p2));
}
/**
* tests the firstDerivative function by comparison
*
* <p>This will test the functions
* {@code f(x) = x^3 - 2x^2 + 6x + 3, g(x) = 3x^2 - 4x + 6}
* and {@code h(x) = 6x - 4}
*/
@Test
public void testMath341() {
double[] f_coeff = { 3, 6, -2, 1 };
double[] g_coeff = { 6, -4, 3 };
double[] h_coeff = { -4, 6 };
PolynomialFunction f = new PolynomialFunction(f_coeff);
PolynomialFunction g = new PolynomialFunction(g_coeff);
PolynomialFunction h = new PolynomialFunction(h_coeff);
// compare f' = g
Assert.assertEquals(f.polynomialDerivative().value(0), g.value(0), tolerance);
Assert.assertEquals(f.polynomialDerivative().value(1), g.value(1), tolerance);
Assert.assertEquals(f.polynomialDerivative().value(100), g.value(100), tolerance);
Assert.assertEquals(f.polynomialDerivative().value(4.1), g.value(4.1), tolerance);
Assert.assertEquals(f.polynomialDerivative().value(-3.25), g.value(-3.25), tolerance);
// compare g' = h
Assert.assertEquals(g.polynomialDerivative().value(FastMath.PI), h.value(FastMath.PI), tolerance);
Assert.assertEquals(g.polynomialDerivative().value(FastMath.E), h.value(FastMath.E), tolerance);
}
public void checkPolynomial(PolynomialFunction p, String reference) {
Assert.assertEquals(reference, p.toString());
}
private void checkNullPolynomial(PolynomialFunction p) {
for (double coefficient : p.getCoefficients()) {
Assert.assertEquals(0, coefficient, 1e-15);
}
}
}