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); }