public override float findRoot(Segment ab, Interpolation F, float X, float e)
{
float a = ab.a;
float b = ab.b;
float fa, fb, fc;
//N = 0;
while (true)
{
fa = F.Calc(a, new LagrangeMethod()) - X;
fb = F.Calc(b, new LagrangeMethod()) - X;
fc = F.Calc((a + b) / 2.0f, new LagrangeMethod()) - X;
if ((b - a) < 2 * e)
break;
if (fc == 0)
break;
// System.Console.WriteLine("x = {0} {1}", b-a, 2 * e);
// N++;
if (fa * fc < 0)
b = (a + b) / 2.0f;
else
a = (a + b) / 2.0f;
}
return (a + b) / 2.0f;
}
public static void print(Function mFunc, Interpolation mIn)
{
Console.WriteLine(" x | f(x_i) | f'(x_i) | f'(x_i)Т - f'(x_i) | f''(x_i) | f''(x_i)Т - f''(x_i)");
// Console.Write(mFunc.f(x) + " ");
for (int i = 0; i < mIn.mPoints.Count; i++)
{
float x = mIn.mPoints[i].x;
float h = (mIn.b - mIn.a) / (mIn.mPoints.Count - 1);
float fx = mFunc.f(x);
float d1 = 0;
float d2 = 0;
// Console.WriteLine(h);
if (i == 0)
d1 = (-3 * mIn.mPoints[i].fx + 4 * mIn.mPoints[i + 1].fx - mIn.mPoints[i + 2].fx) / (2 * h);
else if (i == mIn.mPoints.Count - 1)
d1 = (3 * mIn.mPoints[i].fx - 4 * mIn.mPoints[i - 1].fx + mIn.mPoints[i - 2].fx) / (2 * h);
else
d1 = (mIn.mPoints[i + 1].fx - mIn.mPoints[i - 1].fx) / (2.0f * h);
if (0 < i && i < mIn.mPoints.Count - 1)
d2 = (mIn.mPoints[i + 1].fx - 2 * mIn.mPoints[i].fx + mIn.mPoints[i - 1].fx) / (h * h);
Console.WriteLine("{0,5} {1,10} {2,10} {3,15} {4,15} {5,10}", x, fx, d1, Math.Abs(mFunc.divf(x) - d1),
d2, Math.Abs(mFunc.div2f(x) - d2));
}
}
static void Main(string[] args)
{
System.Console.WriteLine("The problem of the algebraic interpolation.");
Interpolation i1 = new Interpolation();
Interpolation i2 = new Interpolation();
Function f = new EFunction();
float a = 0.0f;
float b = 1.0f;
int m = 10;
int n = 10;
System.Console.Write("Function: ");
f.Print();
System.Console.WriteLine("Segment: [{0}, {1}]", a, b);
System.Console.WriteLine("Params: m = {0}, n = {1}", m, n);
System.Console.WriteLine("Inverse:");
i1.Func = f;
i1.Init(m, n, a, b, true);
System.Console.WriteLine("Normal:");
i2.Func = f;
i2.Init(m, n, a, b, false);
RootSolution rs = new RootSolution();
rs.Init(0.000001f, 0.05f, a, b, false);
rs.Func = i2;
Differential.print(f, i2);
float fx;
while (true)
{
System.Console.WriteLine("Input F");
float x = Convert.ToSingle(System.Console.ReadLine(), System.Globalization.CultureInfo.InvariantCulture);
System.Console.WriteLine("First Solution");
fx = i1.Calc(x, new LagrangeMethod());
System.Console.WriteLine("Pn(x) = {0}", (float)fx);
System.Console.WriteLine("efn(x) = {0}", Math.Abs((float)f.f(fx) - x));
System.Console.WriteLine("Second Solution");
rs.X = x;
List<float> roots = rs.getRoots(new BisectionMethod());
for (int i = 0; i < roots.Count(); i++)
{
fx = roots[i];
System.Console.WriteLine("Pn(x) = {0}", (float)fx);
System.Console.WriteLine("efn(x) = {0}", Math.Abs((float)f.f(fx) - x));
}
}
System.Console.ReadKey();
}
public abstract float findRoot(Segment ab, Interpolation F, float X, float e);
abstract public float findRoot(Segment ab, Interpolation F, float X, float e);