public double[] Solve(double[] X, double[] Y)
{
//step 1: create matrix, let Z - matrix coefficients
var k = X.Length; //???
Console.WriteLine("LSQ Polinomial Method with order {0}", k);
//x for matrix
var z = new double[k, k];
//y for matrix
var zY = new double[k];
for (int i = 0; i < k; i++)
{
for (int j = 0; j < k; j++)
{
double s = 0;
for (int m = 0; m < X.Length; m++)
{
s += Math.Pow(X[m], i + j);
}
z[i, j] = s;
}
double sY = 0;
for (int m = 0; m < X.Length; m++)
{
sY += Y[m] * Math.Pow(X[m], i);
}
zY[i] = sY;
}
Helpers.PrintMatrix("A", z);
Helpers.PrintVector("B", zY);
//step 2: solve matrix
Gauss.computeCoefficents(z, zY);
return(zY);
}
public double[,] Solve(double[] X, double[] Y)
{
Console.WriteLine("Cubic Spline Interpolation Method");
var k = X.Length - 1;
var result = new double[k, 4]; //4 coeff for each spline - a,b,c,d
var h = new double[k];
for (int i = 0; i < k; i++)
{
h[i] = X[i + 1] - X[i];
//ai
result[i, 0] = Y[i];
}
//matrix
var A = new double[k - 1, k - 1]; //c1 = 0 => skip one row
var B = new double[k - 1];
for (int i = 1; i < k; i++)
{
if (i - 2 > 0) //dont calculate c1
{
A[i - 1, i - 2] = h[i - 1]; //hi-1 * ci-1
}
A[i - 1, i - 1] = (h[i - 1] + h[i]) * 2; //2(hi-1 + hi) * ci
if (i + 1 < k)
{
A[i - 1, i] = h[i]; //hi * ci+1
}
B[i - 1] = 3 * ((Y[i + 1] - Y[i]) / h[i] - (Y[i] - Y[i - 1]) / h[i - 1]);
}
Helpers.PrintMatrix("A", A);
Helpers.PrintVector("B", B);
if (B.Length > 2)
{
//B = Thompson.Solve(A, B);
Gauss.computeCoefficents(A, B);
}
else
{
Gauss.computeCoefficents(A, B);
}
for (int i = 1; i < k; i++)
{
result[i, 2] = B[i - 1]; //c
}
for (int i = 0; i < k - 1; i++)
{
var c = result[i, 2];
//calculate b
result[i, 1] = (Y[i + 1] - Y[i] - c * h[i] * h[i] - ((result[i + 1, 2] - c) / 3) * h[i] * h[i]) / h[i];
//calculate d
result[i, 3] = (result[i + 1, 2] - c) / (3 * h[i]);
}
//for last row we calculate b and d from last equation 2cn + 6dnhn = 0
//dn = -2cn/6hn
result[k - 1, 3] = -result[k - 1, 2] / 6 * h[k - 1];
//bn - calculate using dn
result[k - 1, 1] = (Y[k] - Y[k - 1] - result[k - 1, 2] * h[k - 1] * h[k - 1] - result[k - 1, 3] * h[k - 1] * h[k - 1] * h[k - 1]) / h[k - 1];
return(result);
}