/**
* <p>Hermitian matrix is a square matrix with complex entries that are equal to its own conjugate transpose.</p>
*
* <p>a[i,j] = conj(a[j,i])</p>
*
* @param Q The matrix being tested. Not modified.
* @param tol Tolerance.
* @return True if it passes the test.
*/
public static bool isHermitian(ZMatrixRMaj Q, double tol)
{
if (Q.numCols != Q.numRows)
{
return(false);
}
Complex_F64 a = new Complex_F64();
Complex_F64 b = new Complex_F64();
for (int i = 0; i < Q.numCols; i++)
{
for (int j = i; j < Q.numCols; j++)
{
Q.get(i, j, a);
Q.get(j, i, b);
if (Math.Abs(a.real - b.real) > tol)
{
return(false);
}
if (Math.Abs(a.imaginary + b.imaginary) > tol)
{
return(false);
}
}
}
return(true);
}
/**
* 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 ZMatrixRMaj householderVector(ZMatrixRMaj x)
{
ZMatrixRMaj u = (ZMatrixRMaj)x.copy();
double max = CommonOps_ZDRM.elementMaxAbs(u);
CommonOps_ZDRM.elementDivide(u, max, 0, u);
double nx = NormOps_ZDRM.normF(u);
Complex_F64 c = new Complex_F64();
u.get(0, 0, c);
double 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_ZDRM.elementDivide(u, u.getReal(0, 0), u.getImag(0, 0), u);
return(u);
}