/* ------------------------
* Constructor
* ------------------------ */
///<summary>QR Decomposition, computed by Householder reflections.</summary>
///<param name="A">Rectangular matrix</param>
///<returns>Structure to access R and the Householder vectors and compute Q.</returns>
public QRDecomposition(Matrix3 A)
{
// Initialize.
QR = A.ToFloatArray();
m = A.RowLength();
n = A.ColumnLength();
Rdiag = new float[n];
// Main loop.
for (int k = 0; k < n; k++)
{
// Compute 2-norm of k-th column without under/overflow.
float nrm = 0;
for (int i = k; i < m; i++)
{
nrm = Convert.ToSingle(Maths.Hypot(nrm, QR[i, k]));
}
if (nrm != 0)
{
// Form k-th Householder vector.
if (QR[k, k] < 0)
{
nrm = -nrm;
}
for (int i = k; i < m; i++)
{
QR[i, k] /= nrm;
}
QR[k, k] += 1.0f;
// Apply transformation to remaining columns.
for (int j = k + 1; j < n; j++)
{
float s = 0.0f;
for (int i = k; i < m; i++)
{
s += QR[i, k] * QR[i, j];
}
s = -s / QR[k, k];
for (int i = k; i < m; i++)
{
QR[i, j] += s * QR[i, k];
}
}
}
Rdiag[k] = -nrm;
}
}
/// <summary>
/// Symmetric tridiagonal QL algorithm.
/// </summary>
private void tql2()
{
// This is derived from the Algol procedures tql2, by
// Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
// Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutine in EISPACK.
for (int i = 1; i < n; i++)
{
e[i - 1] = e[i];
}
e[n - 1] = 0.0f;
float f = 0.0f;
float tst1 = 0.0f;
float eps = Convert.ToSingle(Math.Pow(2.0, -52));
for (int l = 0; l < n; l++)
{
// Find small subdiagonal element
tst1 = Convert.ToSingle(Math.Max(tst1, Math.Abs(d[l]) + Math.Abs(e[l])));
int m = l;
while (m < n)
{
if (Math.Abs(e[m]) <= eps * tst1)
{
break;
}
m++;
}
// If m == l, d[l] is an eigenvalue,
// otherwise, iterate.
if (m > l)
{
int iter = 0;
do
{
iter = iter + 1; // (Could check iteration count here.)
// Compute implicit shift
float g = d[l];
float p = (d[l + 1] - g) / (2 * e[l]);
float r = Convert.ToSingle(Maths.Hypot(p, 1));
if (p < 0)
{
r = -r;
}
d[l] = e[l] / (p + r);
d[l + 1] = e[l] * (p + r);
float dl1 = d[l + 1];
float h = g - d[l];
for (int i = l + 2; i < n; i++)
{
d[i] -= h;
}
f = f + h;
// Implicit QL transformation.
p = d[m];
float c = 1.0f;
float c2 = c;
float c3 = c;
float el1 = e[l + 1];
float s = 0.0f;
float s2 = 0.0f;
for (int i = m - 1; i >= l; i--)
{
c3 = c2;
c2 = c;
s2 = s;
g = c * e[i];
h = c * p;
r = Convert.ToSingle(Maths.Hypot(p, e[i]));
e[i + 1] = s * r;
s = e[i] / r;
c = p / r;
p = c * d[i] - s * g;
d[i + 1] = h + s * (c * g + s * d[i]);
// Accumulate transformation.
for (int k = 0; k < n; k++)
{
h = Varray[k, i + 1];
Varray[k, i + 1] = s * Varray[k, i] + c * h;
Varray[k, i] = c * Varray[k, i] - s * h;
}
}
p = -s * s2 * c3 * el1 * e[l] / dl1;
e[l] = s * p;
d[l] = c * p;
// Check for convergence.
} while (Math.Abs(e[l]) > eps * tst1);
}
d[l] = d[l] + f;
e[l] = 0.0f;
}
// Sort eigenvalues and corresponding vectors.
for (int i = 0; i < n - 1; i++)
{
int k = i;
float p = d[i];
for (int j = i + 1; j < n; j++)
{
if (d[j] < p)
{
k = j;
p = d[j];
}
}
if (k != i)
{
d[k] = d[i];
d[i] = p;
for (int j = 0; j < n; j++)
{
p = Varray[j, i];
Varray[j, i] = Varray[j, k];
Varray[j, k] = p;
}
}
}
}