defineSuite([ 'Core/QuarticRealPolynomial', 'Core/Math' ], function( QuarticRealPolynomial, CesiumMath) { 'use strict'; it('discriminant throws without a', function() { expect(function() { QuarticRealPolynomial.computeDiscriminant(); }).toThrowDeveloperError(); }); it('discriminant throws without b', function() { expect(function() { QuarticRealPolynomial.computeDiscriminant(1.0); }).toThrowDeveloperError(); }); it('discriminant throws without c', function() { expect(function() { QuarticRealPolynomial.computeDiscriminant(1.0, 1.0); }).toThrowDeveloperError(); }); it('discriminant throws without d', function() { expect(function() { QuarticRealPolynomial.computeDiscriminant(1.0, 1.0, 1.0); }).toThrowDeveloperError(); }); it('discriminant throws without e', function() { expect(function() { QuarticRealPolynomial.computeDiscriminant(1.0, 1.0, 1.0, 1.0); }).toThrowDeveloperError(); }); it('discriminant', function() { var a = 1; var b = 2; var c = 3; var d = 4; var e = 5; var a2 = a * a; var a3 = a2 * a; var b2 = b * b; var b3 = b2 * b; var c2 = c * c; var c3 = c2 * c; var d2 = d * d; var d3 = d2 * d; var e2 = e * e; var e3 = e2 * e; var expected = b2 * c2 * d2 - 4.0 * b3 * d3 - 4.0 * a * c3 * d2 + 18 * a * b * c * d3 - 27.0 * a2 * d2 * d2 + 256.0 * a3 * e3 + e * (18.0 * b3 * c * d - 4.0 * b2 * c3 + 16.0 * a * c2 * c2 - 80.0 * a * b * c2 * d - 6.0 * a * b2 * d2 + 144.0 * a2 * c * d2) + e2 * (144.0 * a * b2 * c - 27.0 * b2 * b2 - 128.0 * a2 * c2 - 192.0 * a2 * b * d); var actual = QuarticRealPolynomial.computeDiscriminant(a, b, c, d, e); expect(actual).toEqual(expected); }); it('real roots throws without a', function() { expect(function() { QuarticRealPolynomial.computeRealRoots(); }).toThrowDeveloperError(); }); it('real roots throws without b', function() { expect(function() { QuarticRealPolynomial.computeRealRoots(1.0); }).toThrowDeveloperError(); }); it('real roots throws without c', function() { expect(function() { QuarticRealPolynomial.computeRealRoots(1.0, 1.0); }).toThrowDeveloperError(); }); it('real roots throws without d', function() { expect(function() { QuarticRealPolynomial.computeRealRoots(1.0, 1.0, 1.0); }).toThrowDeveloperError(); }); it('real roots throws without e', function() { expect(function() { QuarticRealPolynomial.computeRealRoots(1.0, 1.0, 1.0, 1.0); }).toThrowDeveloperError(); }); it('four repeated roots', function() { var roots = QuarticRealPolynomial.computeRealRoots(2.0, -16.0, 48.0, -64.0, 32.0); expect(roots.length).toEqual(4); expect(roots[0]).toEqualEpsilon(2.0, CesiumMath.EPSILON15); expect(roots[1]).toEqualEpsilon(2.0, CesiumMath.EPSILON15); expect(roots[2]).toEqualEpsilon(2.0, CesiumMath.EPSILON15); expect(roots[3]).toEqualEpsilon(2.0, CesiumMath.EPSILON15); }); it('two pairs of repeated roots', function() { var roots = QuarticRealPolynomial.computeRealRoots(2.0, 0.0, -4.0, 0.0, 2.0); expect(roots.length).toEqual(4); expect(roots[0]).toEqualEpsilon(-1.0, CesiumMath.EPSILON15); expect(roots[1]).toEqualEpsilon(-1.0, CesiumMath.EPSILON15); expect(roots[2]).toEqualEpsilon(1.0, CesiumMath.EPSILON15); expect(roots[3]).toEqualEpsilon(1.0, CesiumMath.EPSILON15); }); it('one pair of repeated roots', function() { var roots = QuarticRealPolynomial.computeRealRoots(2.0, -8.0, 16.0, -16.0, 6.0); expect(roots.length).toEqual(2); expect(roots[0]).toEqualEpsilon(1.0, CesiumMath.EPSILON14); expect(roots[1]).toEqualEpsilon(1.0, CesiumMath.EPSILON14); }); it('two unique and one pair of repeated roots', function() { var roots = QuarticRealPolynomial.computeRealRoots(2.0, 8.0, -6.0, -20.0, 16.0); expect(roots.length).toEqual(4); expect(roots[0]).toEqualEpsilon(-4.0, CesiumMath.EPSILON15); expect(roots[1]).toEqualEpsilon(-2.0, CesiumMath.EPSILON15); expect(roots[2]).toEqualEpsilon(1.0, CesiumMath.EPSILON15); expect(roots[3]).toEqualEpsilon(1.0, CesiumMath.EPSILON15); }); it('four unique roots', function() { var roots = QuarticRealPolynomial.computeRealRoots(2.0, 4.0, -26.0, -28.0, 48.0); expect(roots.length).toEqual(4); expect(roots[0]).toEqualEpsilon(-4.0, CesiumMath.EPSILON15); expect(roots[1]).toEqualEpsilon(-2.0, CesiumMath.EPSILON15); expect(roots[2]).toEqualEpsilon(1.0, CesiumMath.EPSILON15); expect(roots[3]).toEqualEpsilon(3.0, CesiumMath.EPSILON15); }); it('complex roots', function() { var roots = QuarticRealPolynomial.computeRealRoots(3.0, -8.0, 14.0, -8.0, 3.0); expect(roots.length).toEqual(0); }); it('cubic case', function() { var roots = QuarticRealPolynomial.computeRealRoots(0.0, 2.0, 6.0, -26.0, -30.0); expect(roots.length).toEqual(3); expect(roots[0]).toEqualEpsilon(-5.0, CesiumMath.EPSILON15); expect(roots[1]).toEqualEpsilon(-1.0, CesiumMath.EPSILON15); expect(roots[2]).toEqualEpsilon(3.0, CesiumMath.EPSILON15); }); it('stability 1', function() { var a = 1.0; var b = -27121.309311434146; var c = 0.0; var d = -26760.571078686513; var e = -1.0; var expected = [ -0.000037368410630733706, 27121.3093478151]; var actual = QuarticRealPolynomial.computeRealRoots(a, b, c, d, e); expect(actual.length).toEqual(expected.length); expect(actual[0]).toEqualEpsilon(expected[0], CesiumMath.EPSILON12); expect(actual[1]).toEqualEpsilon(expected[1], CesiumMath.EPSILON12); }); it('stability 2', function() { var a = -1.0; var b = -26959.661445199898; var c = 0.0; var d = -26675.609408851604; var e = 1.0; var expected = [ -26959.661481901538, 0.000037487427107407711 ]; var actual = QuarticRealPolynomial.computeRealRoots(a, b, c, d, e); expect(actual.length).toEqual(expected.length); expect(actual[0]).toEqualEpsilon(expected[0], CesiumMath.EPSILON11); expect(actual[1]).toEqualEpsilon(expected[1], CesiumMath.EPSILON11); }); it('stability 3', function() { var a = -1.0; var b = 20607.270539372261; var c = 0.0; var d = 20333.159863900513; var e = 1.0; var expected = [ -0.000049180747737409547, 20607.270587253341 ]; var actual = QuarticRealPolynomial.computeRealRoots(a, b, c, d, e); expect(actual.length).toEqual(expected.length); expect(actual[0]).toEqualEpsilon(expected[0], CesiumMath.EPSILON11); expect(actual[1]).toEqualEpsilon(expected[1], CesiumMath.EPSILON11); }); });