/**
* <p>
* Computes the householder vector that is used to create reflector for the column.
* The results are stored in the original matrix.
* </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 computeHouseHolderCol(int blockLength, DSubmatrixD1 Y,
double[] gamma, int i)
{
double max = BlockHouseHolder_DDRB.findMaxCol(blockLength, Y, i);
if (max == 0.0)
{
return(false);
}
else
{
// computes tau and normalizes u by max
double tau = computeTauAndDivideCol(blockLength, Y, i, max);
// divide u by u_0
double u_0 = Y.get(i, i) + tau;
divideElementsCol(blockLength, Y, i, u_0);
gamma[Y.col0 + i] = u_0 / tau;
tau *= max;
// after the reflector is applied the column would be all zeros but be -tau in the first element
Y.set(i, i, -tau);
}
return(true);
}
/**
* <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, DSubmatrixD1 Y,
double[] gamma, int i)
{
double max = BlockHouseHolder_DDRB.findMaxRow(blockLength, Y, i, i + 1);
if (max == 0.0)
{
return(false);
}
else
{
// computes tau and normalizes u by max
double tau = computeTauAndDivideRow(blockLength, Y, i, i + 1, max);
// divide u by u_0
double u_0 = Y.get(i, i + 1) + tau;
VectorOps_DDRB.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);
}