/**
* Computes the p=∞ norm. If A is a matrix then the induced norm is computed.
*
* @param A Matrix or vector.
* @return The norm.
*/
public static double normPInf(DMatrixRMaj A)
{
if (MatrixFeatures_DDRM.isVector(A))
{
return(CommonOps_DDRM.elementMaxAbs(A));
}
else
{
return(inducedPInf(A));
}
}
/**
* Computes the p=2 norm. If A is a matrix then the induced norm is computed. This
* implementation is faster, but more prone to buffer overflow or underflow problems.
*
* @param A Matrix or vector.
* @return The norm.
*/
public static double fastNormP2(DMatrixRMaj A)
{
if (MatrixFeatures_DDRM.isVector(A))
{
return(fastNormF(A));
}
else
{
return(inducedP2(A));
}
}
/**
* <p>
* Creates a reflector from the provided vector and gamma.<br>
* <br>
* Q = I - γ u u<sup>T</sup><br>
* </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.
* @param gamma To produce a reflector gamma needs to be equal to 2/||u||.
* @return An orthogonal reflector.
*/
public static DMatrixRMaj createReflector(DMatrixRMaj u, double gamma)
{
if (!MatrixFeatures_DDRM.isVector(u))
{
throw new ArgumentException("u must be a vector");
}
DMatrixRMaj Q = CommonOps_DDRM.identity(u.getNumElements());
CommonOps_DDRM.multAddTransB(-gamma, u, u, Q);
return(Q);
}
/**
* <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);
}
/**
* An unsafe but faster version of {@link #normP} that calls routines which are faster
* but more prone to overflow/underflow problems.
*
* @param A Vector or matrix whose norm is to be computed.
* @param p The p value of the p-norm.
* @return The computed norm.
*/
public static double fastNormP(DMatrixRMaj A, double p)
{
if (p == 1)
{
return(normP1(A));
}
else if (p == 2)
{
return(fastNormP2(A));
}
else if (double.IsInfinity(p))
{
return(normPInf(A));
}
if (MatrixFeatures_DDRM.isVector(A))
{
return(fastElementP(A, p));
}
else
{
throw new ArgumentException("Doesn't support induced norms yet.");
}
}
