/**
* <p>
* Element wise p-norm:<br>
* <br>
* norm = {∑<sub>i=1:m</sub> ∑<sub>j=1:n</sub> { |a<sub>ij</sub>|<sup>p</sup>}}<sup>1/p</sup>
* </p>
*
* <p>
* This is not the same as the induced p-norm used on matrices, but is the same as the vector p-norm.
* </p>
*
* @param A Matrix. Not modified.
* @param p p value.
* @return The norm's value.
*/
public static double elementP(DMatrix1Row A, double p)
{
if (p == 1)
{
return(CommonOps_DDRM.elementSumAbs(A));
}
if (p == 2)
{
return(normF(A));
}
else
{
double max = CommonOps_DDRM.elementMaxAbs(A);
if (max == 0.0)
{
return(0.0);
}
double total = 0;
int size = A.getNumElements();
for (int i = 0; i < size; i++)
{
double a = A.get(i) / max;
total += Math.Pow(Math.Abs(a), p);
}
return(max * Math.Pow(total, 1.0 / p));
}
}
/**
* <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>
*
* <p>
* In practice {@link VectorVectorMult_DDRM#householder(double, DMatrixD1, DMatrixD1, DMatrixD1)} multHouseholder}
* should be used for performance reasons since there is no need to calculate Q explicitly.
* </p>
*
* @param u A vector. Not modified.
* @return An orthogonal reflector.
*/
public static DMatrixRMaj createReflector(DMatrix1Row u)
{
if (!MatrixFeatures_DDRM.isVector(u))
{
throw new ArgumentException("u must be a vector");
}
double norm = NormOps_DDRM.fastNormF(u);
double gamma = -2.0 / (norm * norm);
DMatrixRMaj Q = CommonOps_DDRM.identity(u.getNumElements());
CommonOps_DDRM.multAddTransB(gamma, u, u, Q);
return(Q);
}