/**
* <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>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)
{
int startQR = j * numRows;
int endQR = startQR + numRows;
startQR += j;
float max = QrHelperFunctions_FDRM.findMax(QR.data, startQR, numRows - j);
if (max == 0.0f)
{
gamma = 0;
error = true;
}
else
{
// computes tau and normalizes u by max
tau = QrHelperFunctions_FDRM.computeTauAndDivide(startQR, endQR, QR.data, max);
// divide u by u_0
float u_0 = QR.data[startQR] + tau;
QrHelperFunctions_FDRM.divideElements(startQR + 1, endQR, QR.data, u_0);
gamma = u_0 / tau;
tau *= max;
QR.data[startQR] = -tau;
}
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
* 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)
{
float[] u = dataQR[j];
// find the largest value in this column
// this is used to normalize the column and mitigate overflow/underflow
float max = QrHelperFunctions_FDRM.findMax(u, j, numRows - j);
if (max == 0.0f)
{
gamma = 0;
error = true;
}
else
{
// computes tau and normalizes u by max
tau = QrHelperFunctions_FDRM.computeTauAndDivide(j, numRows, u, max);
// divide u by u_0
float u_0 = u[j] + tau;
QrHelperFunctions_FDRM.divideElements(j + 1, numRows, u, u_0);
gamma = u_0 / tau;
tau *= max;
u[j] = -tau;
}
gammas[j] = gamma;
}
/**
* <p>
* Computes the householder vector "u" for the first column of submatrix j. The already computed
* norm is used and checks to see if the matrix is singular at this point.
* </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.
* @return false if it is degenerate
*/
protected bool householderPivot(int j)
{
float[] u = dataQR[j];
// find the largest value in this column
// this is used to normalize the column and mitigate overflow/underflow
float max = QrHelperFunctions_FDRM.findMax(u, j, numRows - j);
if (max <= 0)
{
return(false);
}
else
{
// computes tau and normalizes u by max
tau = QrHelperFunctions_FDRM.computeTauAndDivide(j, numRows, u, max);
// divide u by u_0
float u_0 = u[j] + tau;
QrHelperFunctions_FDRM.divideElements(j + 1, numRows, u, u_0);
gamma = u_0 / tau;
tau *= max;
u[j] = -tau;
if (Math.Abs(tau) <= singularThreshold)
{
return(false);
}
}
gammas[j] = gamma;
return(true);
}