/**
* <p>
* Division: result = a / b
* </p>
*
* @param a Complex number. Not modified.
* @param b Complex number. Not modified.
* @param result Storage for output
*/
public static void divide(Complex_F64 a, Complex_F64 b, Complex_F64 result)
{
double norm = b.getMagnitude2();
result.real = (a.real * b.real + a.imaginary * b.imaginary) / norm;
result.imaginary = (a.imaginary * b.real - a.real * b.imaginary) / norm;
}
/**
* <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);
}
