public override object Evaluate()
{
CPolynomial poly = LeftExpression.EvaluateAsCPolynomial();
int order = RightExpression.EvaluateAsInt32();
return(new CMatrix(poly.NthDerivative(order).ToArray()));
}
public override object Evaluate()
{
CPolynomial poly1 = LeftExpression.EvaluateAsCPolynomial();
CPolynomial poly2 = RightExpression.EvaluateAsCPolynomial();
return(new CMatrix(CPolynomial.Modulus(poly1, poly2).ToArray()));
}
public override void Render(IGraphics2DContext context)
{
int n;
double w = context.Viewport.Width;
double h = context.Viewport.Height;
double step = Math.Max(Region.Width / w, Region.Height / h);
double offset_x = Region.X - (w * step - Region.Width) / 2.0;
double offset_y = Region.Y - (h * step - Region.Height) / 2.0;
CPolynomial p = Polynomial;
CPolynomial pd = Polynomial.FirstDerivative();
for (int y = 0; y < h; y++)
{
for (int x = 0; x < w; x++)
{
Complex Z = new Complex(offset_x + x * step, offset_y + y * step);
Complex Delta = Z;
Complex Z1 = Z;
for (n = 0; (n < MaxIterations) && (Complex.Abs(Z) < BailOut) && Complex.Abs(Delta) > 1E-15; n++)
{
Z = Z - p.Evaluate(Z) / pd.Evaluate(Z);
Delta = Z1 - Z;
Z1 = Z;
}
context.PutPixel(x, y, GetColor(Z, n, MaxIterations));
}
}
}
public override object Evaluate()
{
IList <double> xValues = LeftExpression.EvaluateAsRealVector();
IList <double> yValues = RightExpression.EvaluateAsRealVector();
return(new CMatrix(CPolynomial.InterpolatingPolynomial(xValues, yValues).ToArray()));
}
public NewtonBasins(Rectangle region)
{
Region = region;
MaxIterations = 32;
BailOut = 1E15;
Polynomial = new CPolynomial(new double[] { -1, 0, 0, 0, 0, 1 });
}
public void ParseTest_Fail(string s)
{
//action
Action action = () => CPolynomial.Parse(s);
//assert
action.ShouldThrow <FormatException>();
}
public void ParseTest_Success5()
{
//arrange
CPolynomial expected = new CPolynomial(new Complex[] { 3, new Complex(-4, 12.3), 1 });
//action
CPolynomial actual = CPolynomial.Parse("x+3 + x^2-(5-12.3i)*x");
//assert
actual.Should().Be(expected);
}
public void ParseTest_Success2()
{
//arrange
CPolynomial expected = new CPolynomial(new Complex[] { new Complex(0, -0.3) });
//action
CPolynomial actual = CPolynomial.Parse("-0.3i");
//assert
actual.Should().Be(expected);
}
public void ParseTest_Success3()
{
//arrange
CPolynomial expected = new CPolynomial(new Complex[] { 0, 2 });
//action
CPolynomial actual = CPolynomial.Parse("2x");
//assert
actual.Should().Be(expected);
}
public void FirstDerivativeTest_Analytical()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 5, 8, -14, 3, 6, -22 });
CPolynomial expected = new CPolynomial(new Complex[] { 8, -28, 9, 24, -110 });
//action
CPolynomial actual = target.FirstDerivative();
//assert
actual.Should().Be(expected);
}
public void SecondDerivativeTest_Analytical()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 5, 8, -14, 3, 6, -22 });
CPolynomial expected = new CPolynomial(new Complex[] { -28, 18, 72, -440 });
//action
CPolynomial actual = target.SecondDerivative();
//assert
actual.Should().Be(expected);
}
public void ToStringTest()
{
//arrange
CPolynomial poly = new CPolynomial(new Complex[] { 3, 1.1, 1, 0, 0, new Complex(-5, 12.3) });
string expected = "3 + 1.1*t + t^2 + (-5 + 12.3i)*t^5";
//action
var actual = poly.ToString(null, CultureInfo.InvariantCulture, "t");
//assert
actual.Should().Be(expected);
}
public void AntiderivativeTest()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 3, 8, 16 });
CPolynomial expected = new CPolynomial(new Complex[] { 0, 3, 4, 16.0 / 3 });
//action
CPolynomial actual = target.Antiderivative();
//assert
actual.Should().Be(expected);
}
public void AntiderivativeTest()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 3, 8, 16 });
CPolynomial expected = new CPolynomial(new Complex[] { 0, 3, 4, 16.0 / 3 });
//action
CPolynomial actual = target.Antiderivative();
//assert
actual.Should().Be(expected);
}
public void NthDerivativeTest_Analytical()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 5, 8, -14, 3, 6, -22 });
CPolynomial expected = new CPolynomial(new Complex[] { 18, 144, -1320 });
//action
CPolynomial actual = target.NthDerivative(3);
//assert
actual.Should().Be(expected);
}
public void CharacteristicPolynomial()
{
//arrange
double TOL = 10E-6;
CMatrix zero = new CMatrix(_m.RowCount, _m.ColumnCount);
//action
CPolynomial poly = CMatrix.CharacteristicPolynomial(_m);
CMatrix test = poly.Evaluate(_m);
//assert
CMatrix.FuzzyEquals(test, zero, TOL).Should().BeTrue();
}
public void SecondDerivativeTest()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 5, 8, -14, 3, 6, -22 });
Complex c = 3;
Complex expected = -11206;
//action
Complex actual = target.SecondDerivative(c);
//assert
actual.Should().Be(expected);
}
public void FirstDerivativeTest()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 5, 8, -14, 3, 6, -22 });
Complex value = 3;
Complex expected = -8257;
//action
Complex actual = target.FirstDerivative(value);
//assert
actual.Should().Be(expected);
}
/// <summary>
/// Returns a vector of approximate values of roots of a complex polynomial by companion matrix method.
/// </summary>
/// <param name="poly">A complex polynomial.</param>
/// <returns>The approximate values of roots of poly.</returns>
/// <exception cref="System.ArgumentException">
/// Number of elements in coeffs is less than 2 or more than 99.
/// </exception>
public static Complex[] CompanionMatrixRootsFinding(this CPolynomial poly)
{
// Remove zero elements standing at the end.
int lidx = 0;
int ridx = poly.Length - 1;
while (ridx >= 0 && poly[ridx] == Complex.Zero)
{
ridx--;
}
while (lidx < poly.Length && poly[lidx] == Complex.Zero)
{
lidx++;
}
int length = ridx + 1;
if (length < 2 || length > 99)
{
throw new ArgumentException("Number of coefficients must be between 1 and 100.");
}
int rootsCount = length - 1;
Complex[] roots = new Complex[rootsCount];
int n = ridx - lidx;
CMatrix companionMatrix = new CMatrix(n, n);
for (int i = 1; i < n; i++)
{
companionMatrix[i, i - 1] = Complex.One;
}
for (int i = 0; i < n; i++)
{
companionMatrix[i, n - 1] = -poly[lidx + i] / poly[ridx];
}
CMatrix eigenvals = CMatrix.Eigenvalues(companionMatrix);
for (int i = 0; i < n; i++)
{
roots[i] = eigenvals[i];
}
Array.Sort <Complex>(roots, new ComplexComparer());
return(roots);
}
public void LaguerreRootsFindingTest(params double[] nums)
{
//arrange
double TOL = 10E-7;
CPolynomial poly = FromArray(nums);
//action
Complex[] roots = CPolynomial.LaguerreRoots(poly);
//assert
for (int i = 0; i < roots.Length; i++)
{
Complex p = poly.Evaluate(roots[i]);
Complex.Abs(p).Should().BeLessOrEqualTo(TOL);
}
}
public void FromRootsTest()
{
//arrange
double TOL = 10E-10;
Complex[] roots = new Complex[] { 3, 0, 158.3, 13, 8 };
//action
CPolynomial poly = CPolynomial.FromRoots(roots);
//assert
for (int i = 0; i < roots.Length; i++)
{
Complex p = poly.Evaluate(roots[i]);
Complex.Abs(p).Should().BeLessThan(TOL);
}
}
public void ReadXmlTest_Deserialize()
{
//arrange
CPolynomial expected = new CPolynomial(new Complex[] { 3, 10.2, new Complex(3, -0.2), 0, new Complex(2, 35) });
CPolynomial actual;
XmlSerializer serializer = new XmlSerializer(typeof(CPolynomial));
string xml = "<CPolynomial>3 + 10.2*x + (3 - 0.2i)*x^2 + (2 + 35i)*x^4</CPolynomial>";
//action
using (StringReader reader = new StringReader(xml))
{
actual = (CPolynomial)serializer.Deserialize(reader);
}
//assert
actual.Should().Be(expected);
}
public override object Evaluate()
{
CPolynomial poly = LeftExpression.EvaluateAsCPolynomial();
Object x = RightExpression.Evaluate();
if (x is Complex)
{
return(poly.Evaluate((Complex)x));
}
else if (x is CMatrix)
{
return(poly.Evaluate((CMatrix)x));
}
else
{
throw ExceptionHelper.ThrowWrongArgumentType(x);
}
}
public void DivBinomTest()
{
//arrange
double TOL = 1E-10;
CPolynomial f = new CPolynomial(new Complex[] { 3, 0.2, new Complex(3, 8.2), -0.16, new Complex(2.3, 2), 0, 18.3466, 2000 });
Complex c = 346.34645;
Complex r, rtest;
//action
CPolynomial q = CPolynomial.DivBinom(f, c, out r);
f[0] -= r;
CPolynomial qtest = CPolynomial.DivBinom(f, c, out rtest);
//assert
Complex.Abs(rtest).Should().BeLessOrEqualTo(TOL);
q.Should().Be(qtest);
}
public void DivBinomTest()
{
//arrange
double TOL = 1E-10;
CPolynomial f = new CPolynomial(new Complex[] {3, 0.2, new Complex(3, 8.2), -0.16, new Complex(2.3, 2), 0, 18.3466, 2000});
Complex c = 346.34645;
Complex r, rtest;
//action
CPolynomial q = CPolynomial.DivBinom(f, c, out r);
f[0] -= r;
CPolynomial qtest = CPolynomial.DivBinom(f, c, out rtest);
//assert
Complex.Abs(rtest).Should().BeLessOrEqualTo(TOL);
q.Should().Be(qtest);
}
public void InterpolatingPolynomialTest()
{
//arrange
double TOL = 1E-6;
double[] xValues = new double[] { 1, 2.5, 6, 7.9, 18 };
double[] yValues = new double[] { 8.6, 0, -2, 9, 33 };
//action
CPolynomial poly = CPolynomial.InterpolatingPolynomial(xValues, yValues);
//assert
for (int j = 0; j < xValues.Length; j++)
{
Complex val = poly.Evaluate(xValues[j]);
NumericUtil.FuzzyEquals(yValues[j], val, TOL).Should().BeTrue();
}
}
public void WriteXmlTest_Serialize()
{
//arrange
CPolynomial poly = new CPolynomial(new Complex[] { 3, 5.2, new Complex(3, -0.2), 0, new Complex(2, 35) });
string expected = "<CPolynomial>3+5.2*x+(3-0.2i)*x^2+(2+35i)*x^4</CPolynomial>";
XmlSerializer serializer = new XmlSerializer(typeof(CPolynomial));
StringBuilder sb = new StringBuilder();
//action
using (XmlWriter xw = XmlWriter.Create(sb, new XmlWriterSettings {
OmitXmlDeclaration = true
}))
{
serializer.Serialize(xw, poly);
}
//assert
sb.ToString().Should().Be(expected);
}
/// <summary>
/// Returns the value of the complex polynomial evaluated at a specified value.
/// </summary>
/// <param name="poly">The source.</param>
/// <param name="value">A complex square matrix.</param>
/// <returns>The evaluated value of the complex polynomial.</returns>
/// <exception cref="MatrixSizeMismatchException">The matrix value is not square.</exception>
public static CMatrix Evaluate(this CPolynomial poly, CMatrix value)
{
if (!value.IsSquare)
{
throw new MatrixSizeMismatchException("The matrix must be square.");
}
int len = poly.Degree + 1;
int n = value.RowCount;
CMatrix m = CMatrix.Identity(n);
CMatrix result = new CMatrix(n, n);
for (int i = 0; i < len; i++)
{
result += poly[i] * m;
m *= value;
}
return(result);
}
public void DivTest()
{
//arrange
double TOL = 1E-12;
CPolynomial f = new CPolynomial(new Complex[] { new Complex(3467.2, 456), new Complex(2.225, -0.0123), new Complex(46.2, 4.24), new Complex(2, 2), new Complex(12.8, 16.3), new Complex(0, 0), new Complex(22, 347) });
CPolynomial g = new CPolynomial(new Complex[] { new Complex(3, 8.5), new Complex(11, -0.5), new Complex(0, 1), new Complex(1, 2), new Complex(346, 4.365) });
CPolynomial zero = new CPolynomial(1);
CPolynomial r;
CPolynomial q = CPolynomial.Divide(f, g, out r);
CPolynomial rtest = new CPolynomial(1);
//action
CPolynomial qtest = CPolynomial.Divide(f - r, g, out rtest);
//assert
for (int j = 0; j < rtest.Length; j++)
{
Complex.Abs(rtest[j]).Should().BeLessOrEqualTo(TOL);
}
qtest.Should().Be(q);
}
public void DivTest()
{
//arrange
double TOL = 1E-12;
CPolynomial f = new CPolynomial(new Complex[] { new Complex(3467.2, 456), new Complex(2.225, -0.0123), new Complex(46.2 ,4.24), new Complex(2, 2), new Complex(12.8, 16.3), new Complex(0, 0), new Complex(22, 347) });
CPolynomial g = new CPolynomial(new Complex[] { new Complex(3, 8.5), new Complex(11, -0.5), new Complex(0, 1), new Complex(1, 2), new Complex(346, 4.365) });
CPolynomial zero = new CPolynomial(1);
CPolynomial r;
CPolynomial q = CPolynomial.Divide(f, g, out r);
CPolynomial rtest = new CPolynomial(1);
//action
CPolynomial qtest = CPolynomial.Divide(f - r, g, out rtest);
//assert
for (int j = 0; j < rtest.Length; j++)
{
Complex.Abs(rtest[j]).Should().BeLessOrEqualTo(TOL);
}
qtest.Should().Be(q);
}
public void CompanionMatrixRootsFindingTest()
{
//arrange
double TOL = 10E-10;
CPolynomial poly = new CPolynomial(new Complex[]
{
new Complex(122, 14),
new Complex(0, 2.2),
new Complex(14.22, -18.44),
new Complex(1130, 0),
new Complex(14, 14),
new Complex(18, 0.2)
});
//action
Complex[] roots = poly.CompanionMatrixRootsFinding();
//assert
foreach (Complex root in roots)
{
Complex p = poly.Evaluate(root);
Complex.Abs(p).Should().BeLessThan(TOL);
}
}
public void CompanionMatrixRootsFindingTest()
{
//arrange
double TOL = 10E-10;
CPolynomial poly = new CPolynomial(new Complex[]
{
new Complex(122, 14),
new Complex(0, 2.2),
new Complex(14.22, -18.44),
new Complex(1130, 0),
new Complex(14, 14),
new Complex(18, 0.2)
});
//action
Complex[] roots = poly.CompanionMatrixRootsFinding();
//assert
foreach (Complex root in roots)
{
Complex p = poly.Evaluate(root);
Complex.Abs(p).Should().BeLessThan(TOL);
}
}
public override object Evaluate()
{
CPolynomial poly = SubExpression.EvaluateAsCPolynomial();
return(new CMatrix(poly.Roots()));
}
public void FirstDerivativeTest_Analytical()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 5, 8, -14, 3, 6, -22 });
CPolynomial expected = new CPolynomial(new Complex[] {8, -28, 9, 24, -110});
//action
CPolynomial actual = target.FirstDerivative();
//assert
actual.Should().Be(expected);
}
public void NthDerivativeTest_Analytical()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 5, 8, -14, 3, 6, -22 });
CPolynomial expected = new CPolynomial(new Complex[] { 18, 144, -1320 });
//action
CPolynomial actual = target.NthDerivative(3);
//assert
actual.Should().Be(expected);
}
public void ParseTest_Success2()
{
//arrange
CPolynomial expected = new CPolynomial(new Complex[] { new Complex(0, -0.3) });
//action
CPolynomial actual = CPolynomial.Parse("-0.3i");
//assert
actual.Should().Be(expected);
}
public void ParseTest_Success3()
{
//arrange
CPolynomial expected = new CPolynomial(new Complex[] { 0, 2 });
//action
CPolynomial actual = CPolynomial.Parse("2x");
//assert
actual.Should().Be(expected);
}
public void ReadXmlTest_Deserialize()
{
//arrange
CPolynomial expected = new CPolynomial(new Complex[] { 3, 10.2, new Complex(3, -0.2), 0, new Complex(2, 35) });
CPolynomial actual;
XmlSerializer serializer = new XmlSerializer(typeof(CPolynomial));
string xml = "<CPolynomial>3 + 10.2*x + (3 - 0.2i)*x^2 + (2 + 35i)*x^4</CPolynomial>";
//action
using (StringReader reader = new StringReader(xml))
{
actual = (CPolynomial)serializer.Deserialize(reader);
}
//assert
actual.Should().Be(expected);
}
public void SecondDerivativeTest()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 5, 8, -14, 3, 6, -22 });
Complex c = 3;
Complex expected = -11206;
//action
Complex actual = target.SecondDerivative(c);
//assert
actual.Should().Be(expected);
}
public void SecondDerivativeTest_Analytical()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] { 5, 8, -14, 3, 6, -22 });
CPolynomial expected = new CPolynomial(new Complex[] { -28, 18, 72, -440 });
//action
CPolynomial actual = target.SecondDerivative();
//assert
actual.Should().Be(expected);
}
public void ToStringTest()
{
//arrange
CPolynomial poly = new CPolynomial(new Complex[] { 3, 1.1, 1, 0, 0, new Complex(-5, 12.3) });
string expected = "3 + 1.1*t + t^2 + (-5 + 12.3i)*t^5";
//action
var actual = poly.ToString(null, CultureInfo.InvariantCulture, "t");
//assert
actual.Should().Be(expected);
}
public void WriteXmlTest_Serialize()
{
//arrange
CPolynomial poly = new CPolynomial(new Complex[] { 3, 5.2, new Complex(3, -0.2), 0, new Complex(2, 35) });
string expected = "<CPolynomial>3+5.2*x+(3-0.2i)*x^2+(2+35i)*x^4</CPolynomial>";
XmlSerializer serializer = new XmlSerializer(typeof(CPolynomial));
StringBuilder sb = new StringBuilder();
//action
using (XmlWriter xw = XmlWriter.Create(sb, new XmlWriterSettings { OmitXmlDeclaration = true }))
{
serializer.Serialize(xw, poly);
}
//assert
sb.ToString().Should().Be(expected);
}
public override object Evaluate()
{
IList <Complex> roots = SubExpression.EvaluateAsComplexVector();
return(new CMatrix(CPolynomial.FromRoots(roots).ToArray()));
}
public void FirstDerivativeTest()
{
//arrange
CPolynomial target = new CPolynomial(new Complex[] {5, 8, -14, 3, 6, -22});
Complex value = 3;
Complex expected = -8257;
//action
Complex actual = target.FirstDerivative(value);
//assert
actual.Should().Be(expected);
}
public void ParseTest_Success5()
{
//arrange
CPolynomial expected = new CPolynomial(new Complex[] { 3, new Complex(-4, 12.3), 1 });
//action
CPolynomial actual = CPolynomial.Parse("x+3 + x^2-(5-12.3i)*x");
//assert
actual.Should().Be(expected);
}