/**
* Q = I - gamma*u*u<sup>H</sup>
*/
public static ZMatrixRMaj householder(ZMatrixRMaj u, double gamma)
{
int N = u.DataLength / 2;
// u*u^H
ZMatrixRMaj uut = new ZMatrixRMaj(N, N);
VectorVectorMult_ZDRM.outerProdH(u, u, uut);
// foo = -gamma*u*u^H
CommonOps_ZDRM.elementMultiply(uut, -gamma, 0, uut);
// I + foo
for (int i = 0; i < N; i++)
{
int index = (i * uut.numCols + i) * 2;
uut.data[index] = 1 + uut.data[index];
}
return(uut);
}
/**
* <p>
* Unitary matrices have the following properties:<br><br>
* Q*Q<sup>H</sup> = I
* </p>
* <p>
* This is the complex equivalent of orthogonal matrix.
* </p>
*
* @param Q The matrix being tested. Not modified.
* @param tol Tolerance.
* @return True if it passes the test.
*/
public static bool isUnitary(ZMatrixRMaj Q, double tol)
{
if (Q.numRows < Q.numCols)
{
throw new ArgumentException("The number of rows must be more than or equal to the number of columns");
}
Complex_F64 prod = new Complex_F64();
ZMatrixRMaj[] u = CommonOps_ZDRM.columnsToVector(Q, null);
for (int i = 0; i < u.Length; i++)
{
ZMatrixRMaj a = u[i];
VectorVectorMult_ZDRM.innerProdH(a, a, prod);
if (Math.Abs(prod.real - 1) > tol)
{
return(false);
}
if (Math.Abs(prod.imaginary) > tol)
{
return(false);
}
for (int j = i + 1; j < u.Length; j++)
{
VectorVectorMult_ZDRM.innerProdH(a, u[j], prod);
if (!(prod.getMagnitude2() <= tol * tol))
{
return(false);
}
}
}
return(true);
}