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()
{
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 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 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 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 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);
}
}