public override float findRoot(Segment ab, Polynomial F, float e)
{
float a = ab.a;
float b = ab.b;
float fa, fb, fc;
//N = 0;
while (true)
{
fa = F.f(a);
fb = F.f(b);
fc = F.f((a + b) / 2.0f);
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;
}
static void Main(string[] args)
{
Function F = new EFunction();
Console.WriteLine("Approximation of solutions of integrals");
F.Print();
float a = 0;
float b = 1.0f; //b > a
Console.WriteLine("[a,b] = [{0}, {1}]", a, b);
int M = 100;
int N = 3;
Console.WriteLine("M = {0}, N = {1}", M, N);
float[] m = new float[2 * N];
for (int i = 0; i < 2 * N; i++)
{
m[i] = F.m(i, a, b);
Console.WriteLine("m[{0}] = {1}", i, m[i]);
}
Console.WriteLine("Matrix");
float[,] matrix = new float[N, N + 1];
for (int i = 0; i < N; i++)
{
Console.Write("(");
for (int j = 0; j < N; j++)
{
matrix[i, j] = m[N - 1 + i - j];
Console.Write(matrix[i, j] + " ");
}
Console.Write(") (");
matrix[i, N] = -m[N + i];
Console.Write(matrix[i, N] + ")");
Console.WriteLine("");
}
float[] ak = new float[N];
MatrixRoots.get(matrix, ref ak, N);
Console.WriteLine("a[i]:");
for (int i = 0; i < N; i++)
Console.WriteLine("a[{0}] = {1}", i, ak[i]);
Polynomial p = new Polynomial(N, ak);
RootSolution roots = new RootSolution();
roots.Init(0.0001f, -1, a, b, false);
roots.Func = p;
Console.WriteLine("Roots");
List<float> x = roots.getRoots(new BisectionMethod());
for (int i = 0; i < x.Count; i++)
Console.WriteLine("x[{0}] = {1}", i, x[i]);
float[] A = new float[N];
// N == 3
Console.WriteLine("Coefficients");
float sum = 0;
float J = 0;
if (N == 3)
for (int i = 0; i < N; i++)
{
float wk = (x[i] - x[0]) * (x[i] - x[1]) + (x[i] - x[0]) * (x[i] - x[2]) + (x[i] - x[1]) * (x[i] - x[2]);
float integral = m[2] - m[1] * (x[(i + 1) % N] + x[(i + 2) % N]) + m[0] * x[(i + 1) % N] * x[(i + 2) % N];
A[i] = integral / wk;
sum += A[i];
J += A[i] * F.f(x[i]);
Console.WriteLine("A[{0}] = {1}", i, A[i]);
}
else
{
Console.WriteLine("This N({0}) doesnt supported", N);
Console.ReadKey();
return;
}
Console.WriteLine("RESULT:");
Console.WriteLine("|m0 - sum A[i]| = {0}", Math.Abs(m[0] - sum));
Console.WriteLine("J = {0}", J);
Console.ReadKey();
}
public abstract float findRoot(Segment ab, Polynomial F, float e);