/**
* <p>
* Checks to see if a matrix is orthogonal or isometric.
* </p>
*
* @param Q The matrix being tested. Not modified.
* @param tol Tolerance.
* @return True if it passes the test.
*/
public static bool isOrthogonal(DMatrixRMaj 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");
}
DMatrixRMaj[] u = CommonOps_DDRM.columnsToVector(Q, null);
for (int i = 0; i < u.Length; i++)
{
DMatrixRMaj a = u[i];
for (int j = i + 1; j < u.Length; j++)
{
double val = VectorVectorMult_DDRM.innerProd(a, u[j]);
if (!(Math.Abs(val) <= tol))
{
return(false);
}
}
}
return(true);
}
/**
* <p>
* Given matrix A and an eigen vector of A, compute the corresponding eigen value. This is
* the Rayleigh quotient.<br>
* <br>
* x<sup>T</sup>Ax / x<sup>T</sup>x
* </p>
*
*
* @param A Matrix. Not modified.
* @param eigenVector An eigen vector of A. Not modified.
* @return The corresponding eigen value.
*/
public static double computeEigenValue(DMatrixRMaj A, DMatrixRMaj eigenVector)
{
double bottom = VectorVectorMult_DDRM.innerProd(eigenVector, eigenVector);
double top = VectorVectorMult_DDRM.innerProdA(eigenVector, A, eigenVector);
return(top / bottom);
}
/// <summary>
/// Computes the dot product (a.k.a. inner product) between this vector and vector 'v'.
/// </summary>
/// <param name="v">The second vector in the dot product. Not modified.</param>
public override double dot(SimpleMatrixD v)
{
if (!isVector())
{
throw new ArgumentException("'this' matrix is not a vector.");
}
else if (!v.isVector())
{
throw new ArgumentException("'v' matrix is not a vector.");
}
var vm = v.getMatrix();
return(VectorVectorMult_DDRM.innerProd(mat, vm));
}