/**
* Internal function for computing the decomposition.
*/
private bool _decompose()
{
float[] h = QH.data;
for (int k = 0; k < N - 2; k++)
{
// k = column
u[k * 2] = 0;
u[k * 2 + 1] = 0;
float max = QrHelperFunctions_CDRM.extractColumnAndMax(QH, k + 1, N, k, u, 0);
if (max > 0)
{
// -------- set up the reflector Q_k
float gamma = QrHelperFunctions_CDRM.computeTauGammaAndDivide(k + 1, N, u, max, tau);
gammas[k] = gamma;
// divide u by u_0
float real_u_0 = u[(k + 1) * 2] + tau.real;
float imag_u_0 = u[(k + 1) * 2 + 1] + tau.imaginary;
QrHelperFunctions_CDRM.divideElements(k + 2, N, u, 0, real_u_0, imag_u_0);
// write the reflector into the lower left column of the matrix
for (int i = k + 2; i < N; i++)
{
h[(i * N + k) * 2] = u[i * 2];
h[(i * N + k) * 2 + 1] = u[i * 2 + 1];
}
u[(k + 1) * 2] = 1;
u[(k + 1) * 2 + 1] = 0;
// ---------- multiply on the left by Q_k
QrHelperFunctions_CDRM.rank1UpdateMultR(QH, u, 0, gamma, k + 1, k + 1, N, b);
// ---------- multiply on the right by Q_k
QrHelperFunctions_CDRM.rank1UpdateMultL(QH, u, 0, gamma, 0, k + 1, N);
// since the first element in the householder vector is known to be 1
// store the full upper hessenberg
h[((k + 1) * N + k) * 2] = -tau.real * max;
h[((k + 1) * N + k) * 2 + 1] = -tau.imaginary * max;
}
else
{
gammas[k] = 0;
}
}
return(true);
}
/**
* Computes and performs the similar a transform for submatrix k.
*/
private void similarTransform(int k)
{
float[] t = QT.data;
// find the largest value in this column
// this is used to normalize the column and mitigate overflow/underflow
float max = QrHelperFunctions_CDRM.computeRowMax(QT, k, k + 1, N);
if (max > 0)
{
float gamma = QrHelperFunctions_CDRM.computeTauGammaAndDivide(k * N + k + 1, k * N + N, t, max, tau);
gammas[k] = gamma;
// divide u by u_0
float real_u_0 = t[(k * N + k + 1) * 2] + tau.real;
float imag_u_0 = t[(k * N + k + 1) * 2 + 1] + tau.imaginary;
QrHelperFunctions_CDRM.divideElements(k + 2, N, t, k * N, real_u_0, imag_u_0);
// A column is zeroed first. However a row is being used to store because it reduces
// cache misses. Need to compute the conjugate to have the correct householder operation
for (int i = k + 2; i < N; i++)
{
t[(k * N + i) * 2 + 1] = -t[(k * N + i) * 2 + 1];
}
t[(k * N + k + 1) * 2] = 1.0f;
t[(k * N + k + 1) * 2 + 1] = 0;
// ---------- Specialized householder that takes advantage of the symmetry
// QrHelperFunctions_CDRM.rank1UpdateMultR(QT,QT.data,k*N,gamma,k+1,k+1,N,w);
// QrHelperFunctions_CDRM.rank1UpdateMultL(QT,QT.data,k*N,gamma,k+1,k+1,N);
householderSymmetric(k, gamma);
// since the first element in the householder vector is known to be 1
// store the full upper hessenberg
t[(k * N + k + 1) * 2] = -tau.real * max;
t[(k * N + k + 1) * 2 + 1] = -tau.imaginary * max;
}
else
{
gammas[k] = 0;
}
}
