/**
* <p>
* Computes the householder vector from the specified row
* </p>
*
* <p>
* The householder vector 'u' is computed as follows:<br>
* <br>
* u(1) = 1 <br>
* u(i) = x(i)/(τ + x(1))<br>
* </p>
*
* The first element is implicitly assumed to be one and not written.
*
* @return If there was any problems or not. true = no problem.
*/
public static bool computeHouseHolderRow(int blockLength, FSubmatrixD1 Y,
float[] gamma, int i)
{
float max = BlockHouseHolder_FDRB.findMaxRow(blockLength, Y, i, i + 1);
if (max == 0.0f)
{
return(false);
}
else
{
// computes tau and normalizes u by max
float tau = computeTauAndDivideRow(blockLength, Y, i, i + 1, max);
// divide u by u_0
float u_0 = Y.get(i, i + 1) + tau;
VectorOps_FDRB.div_row(blockLength, Y, i, u_0, Y, i, i + 1, Y.col1 - Y.col0);
gamma[Y.row0 + i] = u_0 / tau;
// after the reflector is applied the column would be all zeros but be -tau in the first element
Y.set(i, i + 1, -tau * max);
}
return(true);
}