/**
* Computes the householder vector used in QR decomposition.
*
* u = x / max(x)
* u(0) = u(0) + |u|
* u = u / u(0)
*
* @param x Input vector. Unmodified.
* @return The found householder reflector vector
*/
public static CMatrixRMaj householderVector(CMatrixRMaj x)
{
CMatrixRMaj u = (CMatrixRMaj)x.copy();
float max = CommonOps_CDRM.elementMaxAbs(u);
CommonOps_CDRM.elementDivide(u, max, 0, u);
float nx = NormOps_CDRM.normF(u);
Complex_F32 c = new Complex_F32();
u.get(0, 0, c);
float realTau, imagTau;
if (c.getMagnitude() == 0)
{
realTau = nx;
imagTau = 0;
}
else
{
realTau = c.real / c.getMagnitude() * nx;
imagTau = c.imaginary / c.getMagnitude() * nx;
}
u.set(0, 0, c.real + realTau, c.imaginary + imagTau);
CommonOps_CDRM.elementDivide(u, u.getReal(0, 0), u.getImag(0, 0), u);
return(u);
}
/**
* <p>
* Creates a reflector from the provided vector.<br>
* <br>
* Q = I - γ u u<sup>T</sup><br>
* γ = 2/||u||<sup>2</sup>
* </p>
*
* @param u A vector. Not modified.
* @return An orthogonal reflector.
*/
public static CMatrixRMaj createReflector(CMatrixRMaj u)
{
if (!MatrixFeatures_CDRM.isVector(u))
{
throw new ArgumentException("u must be a vector");
}
float norm = NormOps_CDRM.normF(u);
float gamma = -2.0f / (norm * norm);
CMatrixRMaj Q = CommonOps_CDRM.identity(u.getNumElements());
CommonOps_CDRM.multAddTransB(gamma, 0, u, u, Q);
return(Q);
}