/**
* <p>
* Computes the householder vector "u" for the first column of submatrix j. Note this is
* a specialized householder for this problem. There is some protection against
* overfloaw and underflow.
* </p>
* <p>
* Q = I - γuu<sup>T</sup>
* </p>
* <p>
* This function finds the values of 'u' and 'γ'.
* </p>
*
* @param j Which submatrix to work off of.
*/
protected void householder(int j)
{
double[] u = dataQR[j];
// find the largest value in this column
// this is used to normalize the column and mitigate overflow/underflow
double max = QrHelperFunctions_ZDRM.findMax(u, j, numRows - j);
if (max == 0.0)
{
gamma = 0;
error = true;
}
else
{
// computes tau and gamma, and normalizes u by max
gamma = QrHelperFunctions_ZDRM.computeTauGammaAndDivide(j, numRows, u, max, tau);
// divide u by u_0
// double u_0 = u[j] + tau;
double real_u_0 = u[j * 2] + tau.real;
double imag_u_0 = u[j * 2 + 1] + tau.imaginary;
QrHelperFunctions_ZDRM.divideElements(j + 1, numRows, u, 0, real_u_0, imag_u_0);
tau.real *= max;
tau.imaginary *= max;
u[j * 2] = -tau.real;
u[j * 2 + 1] = -tau.imaginary;
}
gammas[j] = gamma;
}
/**
* <p>
* Computes the householder vector "u" for the first column of submatrix j. Note this is
* a specialized householder for this problem. There is some protection against
* overflow and underflow.
* </p>
* <p>
* Q = I - γuu<sup>H</sup>
* </p>
* <p>
* This function finds the values of 'u' and 'γ'.
* </p>
*
* @param j Which submatrix to work off of.
*/
protected void householder(int j)
{
int startQR = j * numRows;
int endQR = startQR + numRows;
startQR += j;
double max = QrHelperFunctions_ZDRM.findMax(QR.data, startQR, numRows - j);
if (max == 0.0)
{
gamma = 0;
error = true;
}
else
{
// computes tau and normalizes u by max
gamma = QrHelperFunctions_ZDRM.computeTauGammaAndDivide(startQR, endQR, QR.data, max, tau);
// divide u by u_0
double realU0 = QR.data[startQR * 2] + tau.real;
double imagU0 = QR.data[startQR * 2 + 1] + tau.imaginary;
QrHelperFunctions_ZDRM.divideElements(startQR + 1, endQR, QR.data, 0, realU0, imagU0);
tau.real *= max;
tau.imaginary *= max;
QR.data[startQR * 2] = -tau.real;
QR.data[startQR * 2 + 1] = -tau.imaginary;
}
gammas[j] = gamma;
}