public void TestJenkinsTraubRandomNumber()
{
for (var i = 0; i < 200; i++)
{
var count = Generator.RandomNumber(2, 10);
var coeffs = new double[count];
coeffs = coeffs.Select(_ => (double)Generator.RandomNumber(-100, 100)).ToArray();
var poly = coeffs.Aggregate((KtPolynomial) new One(),
(current, ktNumericBase) => current * KtPolynomial.Create(-ktNumericBase, 1));
var roots = poly.Roots();
var fixroots = roots.Select(elem => elem.Round(7).ToComplex().Real).ToArray();
Assert.AreEqual(coeffs.Length, fixroots.Length);
if (!SequenceEqual(coeffs, fixroots))
{
Debug.Print("Polynomial");
Debug.Print(poly.ToString());
Debug.Print("expected");
Generator.DebugArray(coeffs);
Debug.Print("actual");
Generator.DebugArray(fixroots);
Assert.Fail();
}
Assert.IsTrue(SequenceEqual(coeffs, fixroots));
Assert.IsTrue(ContentEqual(coeffs, fixroots));
}
}
public void DifferentTypes()
{
var poly3 = KtPolynomial.Create(2, 1);
Term term1 = poly3;
var poly1 = KtPolynomial.Create(3, 5, 2, 5);
var poly2 = KtPolynomial.Create(3, 12, -2);
Term term2 = new DiscontinuousTerm(poly1, poly2, Limit.Create(-12, 20));
var actualResult = term1 - term2;
Assert.AreEqual(actualResult.Length, 3);
Term expectedResult1 = new DiscontinuousTerm(poly3, KtPolynomial.Create(1), ForwardLimit.Create(-12));
Assert.AreEqual(actualResult[0], expectedResult1);
Term expectedResult2 = new DiscontinuousTerm((poly3 * poly2) - poly1, poly2, Limit.Create(-12, 20));
Assert.AreEqual(actualResult[1], expectedResult2);
Term expectedResult3 = new DiscontinuousTerm(poly3, KtPolynomial.Create(1), BackwardLimit.Create(20));
Assert.AreEqual(actualResult[2], expectedResult3);
actualResult = term2 - term1; //reversed
Assert.AreEqual(actualResult.Length, 3);
expectedResult1 = new DiscontinuousTerm(-poly3, KtPolynomial.Create(1), ForwardLimit.Create(-12));
Assert.AreEqual(actualResult[0], expectedResult1);
expectedResult2 = new DiscontinuousTerm(poly1 - (poly3 * poly2), poly2, Limit.Create(-12, 20));
Assert.AreEqual(actualResult[1], expectedResult2);
expectedResult3 = new DiscontinuousTerm(-poly3, KtPolynomial.Create(1), BackwardLimit.Create(20));
Assert.AreEqual(actualResult[2], expectedResult3);
}
private static Expression RightSideExpression(double a, double b)
{
var L = a + b;
var kteq = KtPolynomial.Create(0, ((a * b * b) / (3 * L)) + ((a * a * b) / (6 * L)), 0, -b / (6 * L));
return(new Expression(kteq));
}
private static Expression LeftSideExpression(double a, double b)
{
var L = a + b;
var kteq = KtPolynomial.Create(-a.RaiseTo(3) / 6, (a.RaiseTo(3) / (6 * L)) + ((L * a) / 3), -a / 2, a / (6 * L));
return(new Expression(kteq));
}
public void TestJenkinsTraub5()
{
var coeff = new Complex[] { 5, -20, 5, 50, -20, -40 };
var expectedRoots = new Number[] { -1, -1, 2, 2, 2.0 };
var roots = KtPolynomial.Create(coeff.Select(elem => (Number)elem).Reverse().ToArray()).Roots();
Assert.AreEqual(expectedRoots.Length, roots.Length);
Assert.IsTrue(SequenceEqual(roots.ToArray(), expectedRoots));
Assert.IsTrue(ContentEqual(roots.ToArray(), expectedRoots));
}
public void TestRoot5746()
{
var coeff = new Number[] { 6, 4, -7, 5 };
var expectedRoots = new Number[] { (1, 1), (1, -1), -3.0 / 5 };
var roots = KtPolynomial.Create(coeff).Roots();
Assert.AreEqual(expectedRoots.Length, roots.Length);
Assert.IsTrue(ContentEqual(roots.ToArray(), expectedRoots));
Assert.IsTrue(SequenceEqual(roots.ToArray(), expectedRoots));
}
public void BothDiscontinuousSpliceable()
{
var poly3 = KtPolynomial.Create(2, 1);
var poly4 = KtPolynomial.Create(3, 1);
Term term1 = new DiscontinuousTerm(poly3, poly4, ForwardLimit.Create(9));
Term term2 = new DiscontinuousTerm(poly3, poly4, BackwardLimit.Create(9));
var actualResult = term1 + term2;
Assert.AreEqual(actualResult.Length, 1);
Assert.AreEqual(actualResult[0], new ContinuousTerm(poly3, poly4));
}
public void MultTest()
{
var poly3 = KtPolynomial.Create(2, 1);
Term term1 = poly3;
var poly1 = KtPolynomial.Create(3, 5, 2, 5);
var poly2 = KtPolynomial.Create(3, 12, -2);
Term term2 = new DiscontinuousTerm(poly1, poly2, Limit.Create(-12, 20));
var actualResult = term1 * term2;
Term expectedResult2 = new DiscontinuousTerm(poly3 * poly1, poly2, Limit.Create(-12, 20));
Assert.AreEqual(actualResult, expectedResult2);
}
public void TestJenkinsTraub2()
{
var coeff = new Complex[] { 1, -3, -2, 6 };
Number[] expectedRoots = { Round(Sqrt(2), 9), -Round(Sqrt(2), 9), 3 };
var roots = KtPolynomial.Create(coeff.Select(elem => (Number)elem).Reverse().ToArray()).Roots();
Assert.AreEqual(expectedRoots.Length, roots.Length);
Assert.IsTrue(roots.Contains(expectedRoots[0]));
Assert.IsTrue(roots.All(expectedRoots.Contains));
Assert.IsTrue(expectedRoots.All(roots.Contains));
Assert.IsTrue(ContentEqual(roots.ToArray(), expectedRoots));
}
public void BothContinuous()
{
var poly1A = KtPolynomial.Create(4, 3, -24, 1);
var poly1B = KtPolynomial.Create(1.134, 3, 33, -12);
var poly2A = KtPolynomial.Create(-3, 45, 2, 4, 3);
var poly2B = KtPolynomial.Create(8, 0, 4, -1);
var cont1 = new ContinuousTerm(poly1A, poly1B);
var cont2 = new ContinuousTerm(poly2A, poly2B);
var actualResult = cont1 - cont2;
Assert.AreEqual(actualResult.Length, 1);
Assert.AreEqual(actualResult[0], new ContinuousTerm((poly1A * poly2B) - (poly1B * poly2A), poly2B * poly1B));
}
public void BothDiscontinuousNotTouching()
{
var poly3 = KtPolynomial.Create(2, 1);
var poly4 = KtPolynomial.Create(3, 1);
Term term1 = new DiscontinuousTerm(poly3, poly4, Limit.Create(-12, 9));
var poly1 = KtPolynomial.Create(3, 5, 2, 5);
var poly2 = KtPolynomial.Create(3, 12, -2);
Term term2 = new DiscontinuousTerm(poly1, poly2, Limit.Create(10, 20));
var actualResult = term1 + term2;
Assert.AreEqual(actualResult.Length, 2);
Assert.AreEqual(actualResult[0], term1);
Assert.AreEqual(actualResult[1], term2);
}
public void GaussianEliminationTest()
{
var mat1 = new Matrix(new[, ] {
{ 1936.0 / 45, 692.0 / 15 },
{ 692.0 / 15, 324.0 / 5 }
});
var polyu = KtPolynomial.Create(1);
var poly1 = KtPolynomial.Create(0, 572.0 / 45, 0, -11.0 / 90);
var poly2 = KtPolynomial.Create(-32.0 / 3, 932.0 / 45, -2, 2.0 / 45);
var expression1 = new Expression(
((poly1, polyu), Limit.Create(0, 4)),
((poly2, polyu), Limit.Create(4, 9)),
((poly2, polyu), Limit.Create(9, 15)));
var poly3 = KtPolynomial.Create(0, 63.0 / 5, 0, -1 / 15.0);
var poly4 = KtPolynomial.Create(-243 / 2.0, 531.0 / 10, -9.0 / 2, 1.0 / 10);
var expression2 = new Expression(
((poly3, polyu), Limit.Create(0, 4)),
((poly3, polyu), Limit.Create(4, 9)),
((poly4, polyu), Limit.Create(9, 15)));
var mat2 = new Matrix(new[, ] {
{ expression1 }, { expression2 }
});
var actual = MatrixMethods.GaussianElimination(mat1, mat2);
//GetEllapsedTime(mat1, mat2);
var expPoly1a = KtPolynomial.Create(0, 2727.0 / 7420, 0, -109.0 / 14840);
var expPoly1b = KtPolynomial.Create(-1944.0 / 1855, 8559.0 / 7420, -729.0 / 3710, 67.0 / 7420);
var expPoly1c = KtPolynomial.Create(3159.0 / 424, -24921.0 / 14840, 351.0 / 2968, -39.0 / 14840);
var expPoly2a = KtPolynomial.Create(0, -374.0 / 5565, 0, 187.0 / 44520);
var expPoly2b = KtPolynomial.Create(1384.0 / 1855, -3488.0 / 5565, 519.0 / 3710, -83.0 / 11130);
var expPoly2c = KtPolynomial.Create(-761.0 / 106, 22427.0 / 11130, -57.0 / 371, 19.0 / 5565);
var expected1 = new Expression(
((expPoly1a, polyu), Limit.Create(0, 4)),
((expPoly1b, polyu), Limit.Create(4, 9)),
((expPoly1c, polyu), Limit.Create(9, 15)));
var expected2 = new Expression(
((expPoly2a, polyu), Limit.Create(0, 4)),
((expPoly2b, polyu), Limit.Create(4, 9)),
((expPoly2c, polyu), Limit.Create(9, 15)));
var expected = new Matrix(new[, ] {
{ expected1 }, { expected2 }
});
Assert.AreEqual(expected1, actual[0, 0]);
Assert.AreEqual(expected2, actual[1, 0]);
Assert.AreEqual(expected, actual);
}
public void MultiplicationOfExpressionAndNumber()
{
var mat1 = new Matrix(new[, ] {
{ 1.0 / 2, -2, -30, 20 },
{ 15, 2.1, 4, 3 },
{ 3, 2, 1, 3 },
{ 4, -4, 3, 2 }
});
var expression1 = new Expression(((KtPolynomial.Create(3, 2), KtPolynomial.Create(1, 2)), Limit.Create(3, 12)));
var expression2 = new Expression(((KtPolynomial.Create(2), KtPolynomial.Create(1, 2)), Limit.Create(3, 12)));
var mat2 = new Matrix(new[, ] {
{ expression1 }, { expression2 }, { expression1 }, { expression2 }
});
_ = mat1 * mat2;
}
public void Subtracting()
{
var poly1 = KtPolynomial.Create(4, 0, -2, 0, 4, 1);
var poly2 = KtPolynomial.Create(3, -4.3, 1);
var poly3 = KtPolynomial.Create(4, 3, 7);
var denom = KtPolynomial.Create(1);
var term1 = new DiscontinuousTerm(poly1, denom, Limit.Create(-20, -10));
var term2 = new DiscontinuousTerm(poly2, denom, Limit.Create(-15, -5));
Term term3 = poly3;
var expression = new Expression(term1, term3, term2);
var actual = expression - expression;
_ = new Zero();
var expected = new Expression((Number)0);
Assert.AreEqual(actual, expected);
}
public void BothDiscontinuousBarelyInclusive()
{
var poly3 = KtPolynomial.Create(2, 1);
var poly4 = KtPolynomial.Create(3, 1);
Term term1 = new DiscontinuousTerm(poly3, poly4, Limit.Create(-12, 10));
var poly1 = KtPolynomial.Create(3, 5, 2, 5);
var poly2 = KtPolynomial.Create(3, 12, -2);
Term term2 = new DiscontinuousTerm(poly1, poly2, Limit.Create(-12, 20));
var actualResult = term1 - term2;
Assert.AreEqual(actualResult.Length, 2);
Term expectedResult2 = new DiscontinuousTerm((poly3 * poly2) - (poly1 * poly4), poly4 * poly2, Limit.Create(-12, 10));
Assert.AreEqual(actualResult[0], expectedResult2);
Term expectedResult3 = new DiscontinuousTerm(-poly1, poly2, Limit.Create(10, 20));
Assert.AreEqual(actualResult[1], expectedResult3);
}
public void Adding()
{
var poly1 = KtPolynomial.Create(4, 0, -2, 0, 4, 1);
var poly2 = KtPolynomial.Create(3, -4.3, 1);
var poly3 = KtPolynomial.Create(4, 3, 7);
var denom = KtPolynomial.Create(1);
var term1 = new DiscontinuousTerm(poly1, denom, Limit.Create(-20, -10));
var term2 = new DiscontinuousTerm(poly2, denom, Limit.Create(-15, -5));
Term term3 = poly3;
var expression = new Expression(term1, term3, term2);
var expected = new Expression(
new DiscontinuousTerm(2 * poly3, denom, ForwardLimit.Create(-20)),
new DiscontinuousTerm(2 * (poly3 + poly1), denom, Limit.Create(-20, -15)),
new DiscontinuousTerm(2 * (poly3 + poly1 + poly2), denom, Limit.Create(-15, -10)),
new DiscontinuousTerm(2 * (poly3 + poly2), denom, Limit.Create(-10, -5)),
new DiscontinuousTerm(2 * poly3, denom, BackwardLimit.Create(-5)));
Assert.AreEqual(expression + expression, expected);
}
public void BothDiscontinuousOverlap()
{
var poly3 = KtPolynomial.Create(2, 1);
var poly4 = KtPolynomial.Create(3, 1);
Term term1 = new DiscontinuousTerm(poly3, poly4, Limit.Create(-12, 15));
var poly1 = KtPolynomial.Create(3, 5, 2, 5);
var poly2 = KtPolynomial.Create(3, 12, -2);
Term term2 = new DiscontinuousTerm(poly1, poly2, Limit.Create(10, 20));
var actualResult = term1 + term2;
Assert.AreEqual(actualResult.Length, 3);
Term term3 = new DiscontinuousTerm(poly3, poly4, Limit.Create(-12, 10));
Term term4 = new DiscontinuousTerm((poly3 * poly2) + (poly1 * poly4), poly4 * poly2, Limit.Create(10, 15));
Term term5 = new DiscontinuousTerm(poly1, poly2, Limit.Create(15, 20));
Assert.AreEqual(actualResult[0], term3);
Assert.AreEqual(actualResult[1], term4);
Assert.AreEqual(actualResult[2], term5);
}
public void ContinuousAndNot()
{
var poly3 = KtPolynomial.Create(2, 1);
Term term1 = poly3;
var poly1 = KtPolynomial.Create(3, 5, 2, 5);
var poly2 = KtPolynomial.Create(3, 12, -2);
Term term2 = new DiscontinuousTerm(poly1, poly2, Limit.Create(-12, 20));
var actualResult = term1 + term2;
Assert.AreEqual(actualResult.Length, 3);
Term expectedResult1 = new DiscontinuousTerm(poly3, KtPolynomial.Create(1), ForwardLimit.Create(-12));
Assert.AreEqual(actualResult[0], expectedResult1);
Term expectedResult2 = new DiscontinuousTerm((poly3 * poly2) + poly1, poly2, Limit.Create(-12, 20));
Assert.AreEqual(actualResult[1], expectedResult2);
Term expectedResult3 = new DiscontinuousTerm(poly3, KtPolynomial.Create(1), BackwardLimit.Create(20));
Assert.AreEqual(actualResult[2], expectedResult3);
Assert.IsTrue(actualResult.SequenceEqual(term2 + term1));
}