public static MatrixR Tridiagonalize(MatrixR A)
{
int n = A.GetCols();
MatrixR A1 = new MatrixR(n, n);
A1 = A.Clone();
double h, g, unorm;
for (int i = 0; i < n - 2; i++)
{
VectorR u = new VectorR(n - i - 1);
for (int j = i + 1; j < n; j++)
{
u[j - i - 1] = A[i, j];
}
unorm = u.GetNorm();
if (u[0] < 0.0)
{
unorm = -unorm;
}
u[0] += unorm;
for (int j = i + 1; j < n; j++)
{
A[j, i] = u[j - i - 1];
}
h = VectorR.DotProduct(u, u) * 0.5;
VectorR v = new VectorR(n - i - 1);
MatrixR a1 = new MatrixR(n - i - 1, n - i - 1);
for (int j = i + 1; j < n; j++)
{
for (int k = i + 1; k < n; k++)
{
a1[j - i - 1, k - i - 1] = A[j, k];
}
}
v = MatrixR.Transform(a1, u) / h;
g = VectorR.DotProduct(u, v) / (2.0 * h);
v -= g * u;
for (int j = i + 1; j < n; j++)
{
for (int k = i + 1; k < n; k++)
{
A[j, k] = A[j, k] - v[j - i - 1] * u[k - i - 1] - u[j - i - 1] * v[k - i - 1];
}
}
A[i, i + 1] = -unorm;
}
Alpha = new double[n];
Beta = new double[n - 1];
Alpha[0] = A[0, 0];
for (int i = 1; i < n; i++)
{
Alpha[i] = A[i, i];
Beta[i - 1] = A[i - 1, i];
}
MatrixR V = new MatrixR(n, n);
V = V.Identity();
for (int i = 0; i < n - 2; i++)
{
VectorR u = new VectorR(n - i - 1);
for (int j = i + 1; j < n; j++)
{
u[j - i - 1] = A.GetColVector(i)[j];
}
h = VectorR.DotProduct(u, u) * 0.5;
VectorR v = new VectorR(n - 1);
MatrixR v1 = new MatrixR(n - 1, n - i - 1);
for (int j = 1; j < n; j++)
{
for (int k = i + 1; k < n; k++)
{
v1[j - 1, k - i - 1] = V[j, k];
}
}
v = MatrixR.Transform(v1, u) / h;
for (int j = 1; j < n; j++)
{
for (int k = i + 1; k < n; k++)
{
V[j, k] -= v[j - 1] * u[k - i - 1];
}
}
}
return(V);
}
