public void testMultiplication() {
PolynomialFunction p1 = new PolynomialFunction(new double[] {-3.0, 2.0});
PolynomialFunction p2 = new PolynomialFunction(new double[] {3.0, 2.0, 1.0});
checkPolynomial(p1.multiply(p2), "-9.0 + x^2 + 2.0 x^3");
p1 = new PolynomialFunction(new double[] {0.0, 1.0});
p2 = p1;
for (int i = 2; i < 10; ++i) {
p2 = p2.multiply(p1);
checkPolynomial(p2, "x^" + i);
}
}
public void testAddition() {
PolynomialFunction p1 = new PolynomialFunction(new double[] {-2.0, 1.0});
PolynomialFunction p2 = new PolynomialFunction(new double[] {2.0, -1.0, 0.0});
checkNullPolynomial(p1.add(p2));
p2 = p1.add(p1);
checkPolynomial(p2, "-4.0 + 2.0 x");
p1 = new PolynomialFunction(new double[] {1.0, -4.0, 2.0});
p2 = new PolynomialFunction(new double[] {-1.0, 3.0, -2.0});
p1 = p1.add(p2);
assertEquals(1, p1.degree());
checkPolynomial(p1, "-x");
}
/**
* tests the value of a constant polynomial.
*
* <p>value of this is 2.5 everywhere.
*/
public void testConstants() throws MathException {
double[] c = {2.5};
PolynomialFunction f = new PolynomialFunction(c);
// verify that we are equal to c[0] at several (nonsymmetric) places
assertEquals(f.value(0.0), c[0], tolerance);
assertEquals(f.value(-1.0), c[0], tolerance);
assertEquals(f.value(-123.5), c[0], tolerance);
assertEquals(f.value(3.0), c[0], tolerance);
assertEquals(f.value(456.89), c[0], tolerance);
assertEquals(f.degree(), 0);
assertEquals(f.derivative().value(0), 0, tolerance);
assertEquals(f.polynomialDerivative().derivative().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)
*/
public void testQuadratic() {
double[] c = {-2.0, -3.0, 2.0};
PolynomialFunction f = new PolynomialFunction(c);
// verify that we are equal to c[0] when x=0
assertEquals(f.value(0.0), c[0], tolerance);
// now check a few other places
assertEquals(0.0, f.value(-0.5), tolerance);
assertEquals(0.0, f.value(2.0), tolerance);
assertEquals(-2.0, f.value(1.5), tolerance);
assertEquals(7.0, f.value(-1.5), tolerance);
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 */
public void testQuintic() {
double[] c = {0.0, 0.0, 15.0, -13.0, -3.0, 1.0};
PolynomialFunction f = new PolynomialFunction(c);
// verify that we are equal to c[0] when x=0
assertEquals(f.value(0.0), c[0], tolerance);
// now check a few other places
assertEquals(0.0, f.value(5.0), tolerance);
assertEquals(0.0, f.value(1.0), tolerance);
assertEquals(0.0, f.value(-3.0), tolerance);
assertEquals(54.84375, f.value(-1.5), tolerance);
assertEquals(-8.06637, f.value(1.3), tolerance);
assertEquals(f.degree(), 5);
}
/**
* tests the value of a linear polynomial.
*
* <p>This will test the function f(x) = 3*x - 1.5
*
* <p>This will have the values <tt>f(0.0) = -1.5, f(-1.0) = -4.5, f(-2.5) = -9.0, f(0.5) = 0.0,
* f(1.5) = 3.0</tt> and <tt>f(3.0) = 7.5</tt>
*/
public void testLinear() throws MathException {
double[] c = {-1.5, 3.0};
PolynomialFunction f = new PolynomialFunction(c);
// verify that we are equal to c[0] when x=0
assertEquals(f.value(0.0), c[0], tolerance);
// now check a few other places
assertEquals(-4.5, f.value(-1.0), tolerance);
assertEquals(-9.0, f.value(-2.5), tolerance);
assertEquals(0.0, f.value(0.5), tolerance);
assertEquals(3.0, f.value(1.5), tolerance);
assertEquals(7.5, f.value(3.0), tolerance);
assertEquals(f.degree(), 1);
assertEquals(f.polynomialDerivative().derivative().value(0), 0, tolerance);
}
public void testSubtraction() {
PolynomialFunction p1 = new PolynomialFunction(new double[] {-2.0, 1.0});
checkNullPolynomial(p1.subtract(p1));
PolynomialFunction p2 = new PolynomialFunction(new double[] {-2.0, 6.0});
p2 = p2.subtract(p1);
checkPolynomial(p2, "5.0 x");
p1 = new PolynomialFunction(new double[] {1.0, -4.0, 2.0});
p2 = new PolynomialFunction(new double[] {-1.0, 3.0, 2.0});
p1 = p1.subtract(p2);
assertEquals(1, p1.degree());
checkPolynomial(p1, "2.0 - 7.0 x");
}
private void checkNullPolynomial(PolynomialFunction p) {
for (double coefficient : p.getCoefficients()) {
assertEquals(0.0, coefficient, 1.0e-15);
}
}
public void checkPolynomial(PolynomialFunction p, String reference) {
assertEquals(reference, p.toString());
}
/**
* tests the firstDerivative function by comparison
*
* <p>This will test the functions <tt>f(x) = x^3 - 2x^2 + 6x + 3, g(x) = 3x^2 - 4x + 6</tt> and
* <tt>h(x) = 6x - 4</tt>
*/
public void testfirstDerivativeComparison() throws MathException {
double[] f_coeff = {3.0, 6.0, -2.0, 1.0};
double[] g_coeff = {6.0, -4.0, 3.0};
double[] h_coeff = {-4.0, 6.0};
PolynomialFunction f = new PolynomialFunction(f_coeff);
PolynomialFunction g = new PolynomialFunction(g_coeff);
PolynomialFunction h = new PolynomialFunction(h_coeff);
// compare f' = g
assertEquals(f.derivative().value(0.0), g.value(0.0), tolerance);
assertEquals(f.derivative().value(1.0), g.value(1.0), tolerance);
assertEquals(f.derivative().value(100.0), g.value(100.0), tolerance);
assertEquals(f.derivative().value(4.1), g.value(4.1), tolerance);
assertEquals(f.derivative().value(-3.25), g.value(-3.25), tolerance);
// compare g' = h
assertEquals(g.derivative().value(Math.PI), h.value(Math.PI), tolerance);
assertEquals(g.derivative().value(Math.E), h.value(Math.E), tolerance);
}