/** Test cornercases with NaN and Infinity. */
public void testNthRoot_cornercase_NAN_Inf() {
// NaN + finite -> NaN
List<Complex> roots = oneNaN.nthRoot(3);
assertEquals(1, roots.size());
assertEquals(Complex.NaN, roots.get(0));
roots = nanZero.nthRoot(3);
assertEquals(1, roots.size());
assertEquals(Complex.NaN, roots.get(0));
// NaN + infinite -> NaN
roots = nanInf.nthRoot(3);
assertEquals(1, roots.size());
assertEquals(Complex.NaN, roots.get(0));
// finite + infinite -> Inf
roots = oneInf.nthRoot(3);
assertEquals(1, roots.size());
assertEquals(Complex.INF, roots.get(0));
// infinite + infinite -> Inf
roots = negInfInf.nthRoot(3);
assertEquals(1, roots.size());
assertEquals(Complex.INF, roots.get(0));
}
/**
* Test: computing <b>third roots</b> of z with real part 0.
*
* <pre>
* <code>
* <b>z = 2 * i</b>
* => z_0 = 1.0911 + 0.6299 * i
* => z_1 = -1.0911 + 0.6299 * i
* => z_2 = -2.3144 - 1.2599 * i
* </code>
* </pre>
*/
public void testNthRoot_cornercase_thirdRoot_realPartZero() {
// complex number with only imaginary part
Complex z = new Complex(0, 2);
// The List holding all third roots
Complex[] thirdRootsOfZ = z.nthRoot(3).toArray(new Complex[0]);
// Returned Collection must not be empty!
assertEquals(3, thirdRootsOfZ.length);
// test z_0
assertEquals(1.0911236359717216, thirdRootsOfZ[0].getReal(), 1.0e-5);
assertEquals(0.6299605249474365, thirdRootsOfZ[0].getImaginary(), 1.0e-5);
// test z_1
assertEquals(-1.0911236359717216, thirdRootsOfZ[1].getReal(), 1.0e-5);
assertEquals(0.6299605249474365, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
// test z_2
assertEquals(-2.3144374213981936E-16, thirdRootsOfZ[2].getReal(), 1.0e-5);
assertEquals(-1.2599210498948732, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
}
/**
* Test: computing <b>third roots</b> of z.
*
* <pre>
* <code>
* <b>z = -2 + 2 * i</b>
* => z_0 = 1 + i
* => z_1 = -1.3660 + 0.3660 * i
* => z_2 = 0.3660 - 1.3660 * i
* </code>
* </pre>
*/
public void testNthRoot_normal_thirdRoot() {
// The complex number we want to compute all third-roots for.
Complex z = new Complex(-2, 2);
// The List holding all third roots
Complex[] thirdRootsOfZ = z.nthRoot(3).toArray(new Complex[0]);
// Returned Collection must not be empty!
assertEquals(3, thirdRootsOfZ.length);
// test z_0
assertEquals(1.0, thirdRootsOfZ[0].getReal(), 1.0e-5);
assertEquals(1.0, thirdRootsOfZ[0].getImaginary(), 1.0e-5);
// test z_1
assertEquals(-1.3660254037844386, thirdRootsOfZ[1].getReal(), 1.0e-5);
assertEquals(0.36602540378443843, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
// test z_2
assertEquals(0.366025403784439, thirdRootsOfZ[2].getReal(), 1.0e-5);
assertEquals(-1.3660254037844384, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
}
/**
* Test: computing <b>third roots</b> of z.
*
* <pre>
* <code>
* <b>z = 8</b>
* => z_0 = 2
* => z_1 = -1 + 1.73205 * i
* => z_2 = -1 - 1.73205 * i
* </code>
* </pre>
*/
public void testNthRoot_cornercase_thirdRoot_imaginaryPartEmpty() {
// The number 8 has three third roots. One we all already know is the number 2.
// But there are two more complex roots.
Complex z = new Complex(8, 0);
// The List holding all third roots
Complex[] thirdRootsOfZ = z.nthRoot(3).toArray(new Complex[0]);
// Returned Collection must not be empty!
assertEquals(3, thirdRootsOfZ.length);
// test z_0
assertEquals(2.0, thirdRootsOfZ[0].getReal(), 1.0e-5);
assertEquals(0.0, thirdRootsOfZ[0].getImaginary(), 1.0e-5);
// test z_1
assertEquals(-1.0, thirdRootsOfZ[1].getReal(), 1.0e-5);
assertEquals(1.7320508075688774, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
// test z_2
assertEquals(-1.0, thirdRootsOfZ[2].getReal(), 1.0e-5);
assertEquals(-1.732050807568877, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
}
/**
* Test: computing <b>fourth roots</b> of z.
*
* <pre>
* <code>
* <b>z = 5 - 2 * i</b>
* => z_0 = 1.5164 - 0.1446 * i
* => z_1 = 0.1446 + 1.5164 * i
* => z_2 = -1.5164 + 0.1446 * i
* => z_3 = -1.5164 - 0.1446 * i
* </code>
* </pre>
*/
public void testNthRoot_normal_fourthRoot() {
// The complex number we want to compute all third-roots for.
Complex z = new Complex(5, -2);
// The List holding all fourth roots
Complex[] fourthRootsOfZ = z.nthRoot(4).toArray(new Complex[0]);
// Returned Collection must not be empty!
assertEquals(4, fourthRootsOfZ.length);
// test z_0
assertEquals(1.5164629308487783, fourthRootsOfZ[0].getReal(), 1.0e-5);
assertEquals(-0.14469266210702247, fourthRootsOfZ[0].getImaginary(), 1.0e-5);
// test z_1
assertEquals(0.14469266210702256, fourthRootsOfZ[1].getReal(), 1.0e-5);
assertEquals(1.5164629308487783, fourthRootsOfZ[1].getImaginary(), 1.0e-5);
// test z_2
assertEquals(-1.5164629308487783, fourthRootsOfZ[2].getReal(), 1.0e-5);
assertEquals(0.14469266210702267, fourthRootsOfZ[2].getImaginary(), 1.0e-5);
// test z_3
assertEquals(-0.14469266210702275, fourthRootsOfZ[3].getReal(), 1.0e-5);
assertEquals(-1.5164629308487783, fourthRootsOfZ[3].getImaginary(), 1.0e-5);
}
