//private Complex Newtone(DoubleOfVectorFunction[] Fns,
// Complex z0, double eps, out int iterations)
//{ //a:=eval(diff(f,x),[x=x0,y=y0]);b:=eval(diff(f,y),[x=x0,y=y0]);d:=eval(f,[x=x0,y=y0]);k(x,y):=a*(x-x0)+b*(y-y0)+d
// double x = z0.re;
// double y = z0.im;
// double x0, y0;
// DoubleOfVectorFunction F = Fns[0];
// DoubleOfVectorFunction G = Fns[1];
// iterations = 0;
// do
// {
// x0 = x;
// y0 = y;
// #region eval {F, G, dFx, dFy, dGx, dGy} @ (x0,y0)
// double F0 = F(x0, y0);
// double G0 = G(x0, y0);
// double dFx0 = dFx(F, x0, y0);
// double dFy0 = dFy(F, x0, y0);
// double dGx0 = dFx(G, x0, y0);
// double dGy0 = dFy(G, x0, y0);
// double t = -dGx0 * dFy0 + dFx0 * dGy0;
// if (t == 0)
// return Complex.NaN;
// if (double.IsNaN(t))
// return Complex.NaN;
// #endregion
// x = (G0 * dFy0 - dGy0 * F0) / t + x0;
// y = (dGx0 * F0 - dFx0 * G0) / t + y0;
// if (++iterations % 200 == 0)
// return Complex.NaN;
// } while (Math.Sqrt((x - x0) * (x - x0) + (y - y0) * (y - y0)) >= eps);
// return new Complex(x, y);
//}
private Complex Newtone(DoubleOfVectorFunction[] Fns,
Complex z0, double eps, out int iterations)
{ //a:=eval(diff(f,x),[x=x0,y=y0]);
//b:=eval(diff(f,y),[x=x0,y=y0]);
//d:=eval(f,[x=x0,y=y0]);
//k(x,y):=a*(x-x0)+b*(y-y0)+d
double x = z0.re;
double y = z0.im;
double x0, y0;
DoubleOfVectorFunction F = Fns[0];
DoubleOfVectorFunction G = Fns[1];
iterations = 0;
do
{
x0 = x;
y0 = y;
#region eval {F, G, dFx, dFy, dGx, dGy} @ (x0,y0)
double F0 = f1(x0, y0);
double G0 = f2(x0, y0);
double dFx0 = df1x(x0, y0);
double dFy0 = df1y(x0, y0);
double dGx0 = df2x(x0, y0);
double dGy0 = df2y(x0, y0);
double t = -dGx0 * dFy0 + dFx0 * dGy0;
if (t == 0)
{
return(Complex.NaN);
}
if (double.IsNaN(t))
{
return(Complex.NaN);
}
#endregion
x = (G0 * dFy0 - dGy0 * F0) / t + x0;
y = (dGx0 * F0 - dFx0 * G0) / t + y0;
if (++iterations % 200 == 0)
{
return(Complex.NaN);
}
} while (Math.Abs(x - x0) >= eps || Math.Abs(y - y0) >= eps);
//} while (Math.Sqrt((x - x0) * (x - x0) + (y - y0) * (y - y0)) >= eps);
return(new Complex(x, y));
}
private void FindRoot()
{
Complex res = Complex.NaN;
#region prepare dform
if (dForm == null)
{
dForm = new DekartForm(100, 100, 300, 300);
dForm.ClientSize = new Size(600, 600);
dForm.Use_IsVisible = false;
dForm.FormClosed += new FormClosedEventHandler(delegate(object s, FormClosedEventArgs eva)
{
dForm = null;
});
}
else
{
dForm.RemoveAllGraphics();
}
#endregion
List <Root> roots = new List <Root>();
List <PointF> pts = new List <PointF>();
List <Color> colors = new List <Color>();
Color[] baseColors = new Color[] {
Color.Red,
Color.Orange,
Color.Yellow,
Color.Green,
Color.LightBlue,
Color.Blue,
Color.Violet
};
double y1 = x1, y2 = x2;
DoubleOfVectorFunction[] dovf = new DoubleOfVectorFunction[] { f1, f2 };
Complex c = new Complex(0);
for (double y = y1; y < y2; y += hy)
{
for (double x = x1; x < x2; x += hx)
{
int iterations;
float percent;
c.re = x;
c.im = y;
res = Newtone(dovf, c, eps, out iterations);
bool inRange = true;
inRange &= res.re > x1;
inRange &= res.re < x2;
inRange &= res.im > y1;
inRange &= res.im < y2;
if (Complex.IsNaN(res) || !inRange)
{
colors.Add(Color.Black);
pts.Add(new PointF((float)x, (float)y));
}
else
{
if (roots.Count == 0)
{
Root newRoot;
newRoot.color = baseColors[roots.Count % baseColors.Length];
newRoot.value = res;
roots.Add(newRoot);
}
percent = iterations / 15f;
if (percent > 1f)
{
percent = 1f;
}
bool needAdd = true;
foreach (Root r in roots)
{
if (Near(r.value, res))
{
colors.Add(ColorModifer.Brightness(r.color, percent));
pts.Add(new PointF((float)x, (float)y));
needAdd = false;
break;
}
}
if (needAdd)
{
Root newRoot;
newRoot.color = baseColors[roots.Count % baseColors.Length];
newRoot.value = res;
roots.Add(newRoot);
colors.Add(ColorModifer.Brightness(newRoot.color, percent));
pts.Add(new PointF((float)x, (float)y));
}
}
}
}
DotGraphic dotGraphic = new DotGraphic(pts.ToArray(), colors.ToArray());
dotGraphic.CurrentColorSchema = new MathGraphic.ColorSchema(
Color.Black, Color.DimGray, Color.DimGray, Color.Gray);
dForm.AddGraphic(dotGraphic);
MathGraphic mg;
mg = new MathGraphic(Color.White, DrawModes.DrawLines, f1x, f1y,
-5f, 5f, 0.01f);
dForm.AddGraphic(mg);
mg = new MathGraphic(Color.White, DrawModes.DrawLines, f2x, f2y,
-5f, 5f, 0.01f);
dForm.AddGraphic(mg);
dForm.Show();
dForm.Update2();
foreach (Root z in roots)
{
listRoots.Items.Add("z" + (listRoots.Items.Count + 1) + " = "
+ z.value.ToString("F6"));
listY.Items.Add("f,g" + (listY.Items.Count + 1) + " = "
+ f1(z.value.re, z.value.im).ToString("F6") + ", "
+ f2(z.value.re, z.value.im).ToString("F6"));
}
}
double dFy(DoubleOfVectorFunction f, params double[] z)
{
return((f(z[0], z[1] + h) - f(z[0], z[1] - h)) / 2 / h);
}
double dFx(DoubleOfVectorFunction f, params double[] z)
{
return((f(z[0] + h, z[1]) - f(z[0] - h, z[1])) / 2 / h);
}
