public Polynomial Smoothing(int n)
{
Polynomial res = new Polynomial(n);
Matrix matrix = new Matrix(n + 1, n + 1);
Vector vect = new Vector(n + 1);
double[] C = new double[2 * n + 1];
for (int m = 0; m < 2 * n + 1; ++m)
{
double sum = 0;
for (int i = 0; i < N; ++i)
{
sum += Math.Pow(tabl[0, i], m);
}
C[m] = sum;
}
for (int k = 0; k < n + 1; ++k)
{
double sum = 0;
for (int i = 0; i < N; ++i)
{
sum += tabl[1, i] * Math.Pow(tabl[0, i], k);
}
vect[k] = sum;
}
for (int i = 0; i < n + 1; ++i)
{
matrix[i, i] = C[i + i];
for (int j = i + 1; j < n + 1; ++j)
{
matrix[i, j] = C[i + j];
matrix[j, i] = C[i + j];
}
}
SLAE lsolve = new SLAE(matrix, vect);
Vector aprmn = lsolve.GaussMethod();
for (int i = 0; i < aprmn.N; i++)
{
res[i] = aprmn[i];
}
return(res);
}
public Polynomial[] Spline()
{
Polynomial[] polinoms = new Polynomial[N - 1];
double h = tabl[0, 1] - tabl[0, 0];
double[] C = new double[N];
C[0] = 0;
C[N - 1] = 0;
Matrix mat = new Matrix(N - 2, N - 2);
Vector vet = new Vector(N - 2);
Vector result;
for (int i = 0; i < mat.M; ++i)
{
mat[i, i] = 4 * h;
if (i < mat.M - 1)
{
mat[i, i + 1] = h;
mat[i + 1, i] = h;
}
vet[i] = (3 / h) * (tabl[1, i + 2] - 2 * tabl[1, i + 1] + tabl[1, i]);
}
if (mat.M != 0)
{
SLAE re = new SLAE(mat, vet);
result = re.Sweeps();
for (int i = 0; i < result.N; ++i)
{
C[i + 1] = result[i];
}
}
Matrix odds = new Matrix(N - 1, 4);
for (int i = 0; i < N - 1; ++i)
{
odds[i, 0] = tabl[1, i];
odds[i, 1] = ((tabl[1, i + 1] - tabl[1, i]) / h) - ((C[i + 1] + 2 * C[i]) * h) / 3;
odds[i, 2] = C[i];
odds[i, 3] = (C[i + 1] - C[i]) / (3 * h);
}
for (int k = 0; k < N - 1; ++k)
{
Polynomial res = new Polynomial(0);
res[0] = 0;
for (int i = 0; i < 4; ++i)
{
Polynomial pol = new Polynomial(0);
pol[0] = odds[k, i];
for (int j = 0; j < i; j++)
{
Polynomial pol2 = new Polynomial(1);
pol2[0] = -tabl[0, k];
pol2[1] = 1;
pol = pol * pol2;
}
res = res + pol;
}
polinoms[k] = res;
}
return(polinoms);
}
